{"id":"node_modules/mathjs/es/function/algebra/derivative.js","dependencies":[{"name":"/home/hernan/workspace/tests/test-simulador/package.json","includedInParent":true,"mtime":1597264365661},{"name":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/package.json","includedInParent":true,"mtime":1593627585935},{"name":"../../utils/is","loc":{"line":1,"column":39},"parent":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/function/algebra/derivative.js","resolved":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/utils/is.js"},{"name":"../../utils/factory","loc":{"line":2,"column":24},"parent":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/function/algebra/derivative.js","resolved":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/utils/factory.js"}],"generated":{"js":"\"use strict\";\n\nObject.defineProperty(exports, \"__esModule\", {\n  value: true\n});\nexports.createDerivative = void 0;\n\nvar _is = require(\"../../utils/is\");\n\nvar _factory = require(\"../../utils/factory\");\n\nvar name = 'derivative';\nvar dependencies = ['typed', 'config', 'parse', 'simplify', 'equal', 'isZero', 'numeric', 'ConstantNode', 'FunctionNode', 'OperatorNode', 'ParenthesisNode', 'SymbolNode'];\nvar createDerivative = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {\n  var typed = _ref.typed,\n      config = _ref.config,\n      parse = _ref.parse,\n      simplify = _ref.simplify,\n      equal = _ref.equal,\n      isZero = _ref.isZero,\n      numeric = _ref.numeric,\n      ConstantNode = _ref.ConstantNode,\n      FunctionNode = _ref.FunctionNode,\n      OperatorNode = _ref.OperatorNode,\n      ParenthesisNode = _ref.ParenthesisNode,\n      SymbolNode = _ref.SymbolNode;\n  /**\n   * Takes the derivative of an expression expressed in parser Nodes.\n   * The derivative will be taken over the supplied variable in the\n   * second parameter. If there are multiple variables in the expression,\n   * it will return a partial derivative.\n   *\n   * This uses rules of differentiation which can be found here:\n   *\n   * - [Differentiation rules (Wikipedia)](https://en.wikipedia.org/wiki/Differentiation_rules)\n   *\n   * Syntax:\n   *\n   *     derivative(expr, variable)\n   *     derivative(expr, variable, options)\n   *\n   * Examples:\n   *\n   *     math.derivative('x^2', 'x')                     // Node {2 * x}\n   *     math.derivative('x^2', 'x', {simplify: false})  // Node {2 * 1 * x ^ (2 - 1)\n   *     math.derivative('sin(2x)', 'x'))                // Node {2 * cos(2 * x)}\n   *     math.derivative('2*x', 'x').evaluate()          // number 2\n   *     math.derivative('x^2', 'x').evaluate({x: 4})    // number 8\n   *     const f = math.parse('x^2')\n   *     const x = math.parse('x')\n   *     math.derivative(f, x)                           // Node {2 * x}\n   *\n   * See also:\n   *\n   *     simplify, parse, evaluate\n   *\n   * @param  {Node | string} expr           The expression to differentiate\n   * @param  {SymbolNode | string} variable The variable over which to differentiate\n   * @param  {{simplify: boolean}} [options]\n   *                         There is one option available, `simplify`, which\n   *                         is true by default. When false, output will not\n   *                         be simplified.\n   * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode}    The derivative of `expr`\n   */\n\n  var derivative = typed('derivative', {\n    'Node, SymbolNode, Object': function NodeSymbolNodeObject(expr, variable, options) {\n      var constNodes = {};\n      constTag(constNodes, expr, variable.name);\n\n      var res = _derivative(expr, constNodes);\n\n      return options.simplify ? simplify(res) : res;\n    },\n    'Node, SymbolNode': function NodeSymbolNode(expr, variable) {\n      return derivative(expr, variable, {\n        simplify: true\n      });\n    },\n    'string, SymbolNode': function stringSymbolNode(expr, variable) {\n      return derivative(parse(expr), variable);\n    },\n    'string, SymbolNode, Object': function stringSymbolNodeObject(expr, variable, options) {\n      return derivative(parse(expr), variable, options);\n    },\n    'string, string': function stringString(expr, variable) {\n      return derivative(parse(expr), parse(variable));\n    },\n    'string, string, Object': function stringStringObject(expr, variable, options) {\n      return derivative(parse(expr), parse(variable), options);\n    },\n    'Node, string': function NodeString(expr, variable) {\n      return derivative(expr, parse(variable));\n    },\n    'Node, string, Object': function NodeStringObject(expr, variable, options) {\n      return derivative(expr, parse(variable), options);\n    } // TODO: replace the 8 signatures above with 4 as soon as typed-function supports optional arguments\n\n    /* TODO: implement and test syntax with order of derivatives -> implement as an option {order: number}\n    'Node, SymbolNode, ConstantNode': function (expr, variable, {order}) {\n      let res = expr\n      for (let i = 0; i < order; i++) {\n        let constNodes = {}\n        constTag(constNodes, expr, variable.name)\n        res = _derivative(res, constNodes)\n      }\n      return res\n    }\n    */\n\n  });\n  derivative._simplify = true;\n\n  derivative.toTex = function (deriv) {\n    return _derivTex.apply(null, deriv.args);\n  }; // FIXME: move the toTex method of derivative to latex.js. Difficulty is that it relies on parse.\n  // NOTE: the optional \"order\" parameter here is currently unused\n\n\n  var _derivTex = typed('_derivTex', {\n    'Node, SymbolNode': function NodeSymbolNode(expr, x) {\n      if ((0, _is.isConstantNode)(expr) && (0, _is.typeOf)(expr.value) === 'string') {\n        return _derivTex(parse(expr.value).toString(), x.toString(), 1);\n      } else {\n        return _derivTex(expr.toString(), x.toString(), 1);\n      }\n    },\n    'Node, ConstantNode': function NodeConstantNode(expr, x) {\n      if ((0, _is.typeOf)(x.value) === 'string') {\n        return _derivTex(expr, parse(x.value));\n      } else {\n        throw new Error(\"The second parameter to 'derivative' is a non-string constant\");\n      }\n    },\n    'Node, SymbolNode, ConstantNode': function NodeSymbolNodeConstantNode(expr, x, order) {\n      return _derivTex(expr.toString(), x.name, order.value);\n    },\n    'string, string, number': function stringStringNumber(expr, x, order) {\n      var d;\n\n      if (order === 1) {\n        d = '{d\\\\over d' + x + '}';\n      } else {\n        d = '{d^{' + order + '}\\\\over d' + x + '^{' + order + '}}';\n      }\n\n      return d + \"\\\\left[\".concat(expr, \"\\\\right]\");\n    }\n  });\n  /**\n   * Does a depth-first search on the expression tree to identify what Nodes\n   * are constants (e.g. 2 + 2), and stores the ones that are constants in\n   * constNodes. Classification is done as follows:\n   *\n   *   1. ConstantNodes are constants.\n   *   2. If there exists a SymbolNode, of which we are differentiating over,\n   *      in the subtree it is not constant.\n   *\n   * @param  {Object} constNodes  Holds the nodes that are constant\n   * @param  {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n   * @param  {string} varName     Variable that we are differentiating\n   * @return {boolean}  if node is constant\n   */\n  // TODO: can we rewrite constTag into a pure function?\n\n\n  var constTag = typed('constTag', {\n    'Object, ConstantNode, string': function ObjectConstantNodeString(constNodes, node) {\n      constNodes[node] = true;\n      return true;\n    },\n    'Object, SymbolNode, string': function ObjectSymbolNodeString(constNodes, node, varName) {\n      // Treat other variables like constants. For reasoning, see:\n      //   https://en.wikipedia.org/wiki/Partial_derivative\n      if (node.name !== varName) {\n        constNodes[node] = true;\n        return true;\n      }\n\n      return false;\n    },\n    'Object, ParenthesisNode, string': function ObjectParenthesisNodeString(constNodes, node, varName) {\n      return constTag(constNodes, node.content, varName);\n    },\n    'Object, FunctionAssignmentNode, string': function ObjectFunctionAssignmentNodeString(constNodes, node, varName) {\n      if (node.params.indexOf(varName) === -1) {\n        constNodes[node] = true;\n        return true;\n      }\n\n      return constTag(constNodes, node.expr, varName);\n    },\n    'Object, FunctionNode | OperatorNode, string': function ObjectFunctionNodeOperatorNodeString(constNodes, node, varName) {\n      if (node.args.length > 0) {\n        var isConst = constTag(constNodes, node.args[0], varName);\n\n        for (var i = 1; i < node.args.length; ++i) {\n          isConst = constTag(constNodes, node.args[i], varName) && isConst;\n        }\n\n        if (isConst) {\n          constNodes[node] = true;\n          return true;\n        }\n      }\n\n      return false;\n    }\n  });\n  /**\n   * Applies differentiation rules.\n   *\n   * @param  {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n   * @param  {Object} constNodes  Holds the nodes that are constant\n   * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode}    The derivative of `expr`\n   */\n\n  var _derivative = typed('_derivative', {\n    'ConstantNode, Object': function ConstantNodeObject(node) {\n      return createConstantNode(0);\n    },\n    'SymbolNode, Object': function SymbolNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      return createConstantNode(1);\n    },\n    'ParenthesisNode, Object': function ParenthesisNodeObject(node, constNodes) {\n      return new ParenthesisNode(_derivative(node.content, constNodes));\n    },\n    'FunctionAssignmentNode, Object': function FunctionAssignmentNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      return _derivative(node.expr, constNodes);\n    },\n    'FunctionNode, Object': function FunctionNodeObject(node, constNodes) {\n      if (node.args.length !== 1) {\n        funcArgsCheck(node);\n      }\n\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      var arg0 = node.args[0];\n      var arg1;\n      var div = false; // is output a fraction?\n\n      var negative = false; // is output negative?\n\n      var funcDerivative;\n\n      switch (node.name) {\n        case 'cbrt':\n          // d/dx(cbrt(x)) = 1 / (3x^(2/3))\n          div = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [createConstantNode(3), new OperatorNode('^', 'pow', [arg0, new OperatorNode('/', 'divide', [createConstantNode(2), createConstantNode(3)])])]);\n          break;\n\n        case 'sqrt':\n        case 'nthRoot':\n          // d/dx(sqrt(x)) = 1 / (2*sqrt(x))\n          if (node.args.length === 1) {\n            div = true;\n            funcDerivative = new OperatorNode('*', 'multiply', [createConstantNode(2), new FunctionNode('sqrt', [arg0])]);\n          } else if (node.args.length === 2) {\n            // Rearrange from nthRoot(x, a) -> x^(1/a)\n            arg1 = new OperatorNode('/', 'divide', [createConstantNode(1), node.args[1]]); // Is a variable?\n\n            constNodes[arg1] = constNodes[node.args[1]];\n            return _derivative(new OperatorNode('^', 'pow', [arg0, arg1]), constNodes);\n          }\n\n          break;\n\n        case 'log10':\n          arg1 = createConstantNode(10);\n\n        /* fall through! */\n\n        case 'log':\n          if (!arg1 && node.args.length === 1) {\n            // d/dx(log(x)) = 1 / x\n            funcDerivative = arg0.clone();\n            div = true;\n          } else if (node.args.length === 1 && arg1 || node.args.length === 2 && constNodes[node.args[1]] !== undefined) {\n            // d/dx(log(x, c)) = 1 / (x*ln(c))\n            funcDerivative = new OperatorNode('*', 'multiply', [arg0.clone(), new FunctionNode('log', [arg1 || node.args[1]])]);\n            div = true;\n          } else if (node.args.length === 2) {\n            // d/dx(log(f(x), g(x))) = d/dx(log(f(x)) / log(g(x)))\n            return _derivative(new OperatorNode('/', 'divide', [new FunctionNode('log', [arg0]), new FunctionNode('log', [node.args[1]])]), constNodes);\n          }\n\n          break;\n\n        case 'pow':\n          constNodes[arg1] = constNodes[node.args[1]]; // Pass to pow operator node parser\n\n          return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes);\n\n        case 'exp':\n          // d/dx(e^x) = e^x\n          funcDerivative = new FunctionNode('exp', [arg0.clone()]);\n          break;\n\n        case 'sin':\n          // d/dx(sin(x)) = cos(x)\n          funcDerivative = new FunctionNode('cos', [arg0.clone()]);\n          break;\n\n        case 'cos':\n          // d/dx(cos(x)) = -sin(x)\n          funcDerivative = new OperatorNode('-', 'unaryMinus', [new FunctionNode('sin', [arg0.clone()])]);\n          break;\n\n        case 'tan':\n          // d/dx(tan(x)) = sec(x)^2\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('sec', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'sec':\n          // d/dx(sec(x)) = sec(x)tan(x)\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('tan', [arg0.clone()])]);\n          break;\n\n        case 'csc':\n          // d/dx(csc(x)) = -csc(x)cot(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('cot', [arg0.clone()])]);\n          break;\n\n        case 'cot':\n          // d/dx(cot(x)) = -csc(x)^2\n          negative = true;\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('csc', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'asin':\n          // d/dx(asin(x)) = 1 / sqrt(1 - x^2)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])]);\n          break;\n\n        case 'acos':\n          // d/dx(acos(x)) = -1 / sqrt(1 - x^2)\n          div = true;\n          negative = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])]);\n          break;\n\n        case 'atan':\n          // d/dx(atan(x)) = 1 / (x^2 + 1)\n          div = true;\n          funcDerivative = new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)]);\n          break;\n\n        case 'asec':\n          // d/dx(asec(x)) = 1 / (|x|*sqrt(x^2 - 1))\n          div = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acsc':\n          // d/dx(acsc(x)) = -1 / (|x|*sqrt(x^2 - 1))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acot':\n          // d/dx(acot(x)) = -1 / (x^2 + 1)\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)]);\n          break;\n\n        case 'sinh':\n          // d/dx(sinh(x)) = cosh(x)\n          funcDerivative = new FunctionNode('cosh', [arg0.clone()]);\n          break;\n\n        case 'cosh':\n          // d/dx(cosh(x)) = sinh(x)\n          funcDerivative = new FunctionNode('sinh', [arg0.clone()]);\n          break;\n\n        case 'tanh':\n          // d/dx(tanh(x)) = sech(x)^2\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('sech', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'sech':\n          // d/dx(sech(x)) = -sech(x)tanh(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('tanh', [arg0.clone()])]);\n          break;\n\n        case 'csch':\n          // d/dx(csch(x)) = -csch(x)coth(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('coth', [arg0.clone()])]);\n          break;\n\n        case 'coth':\n          // d/dx(coth(x)) = -csch(x)^2\n          negative = true;\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('csch', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'asinh':\n          // d/dx(asinh(x)) = 1 / sqrt(x^2 + 1)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])]);\n          break;\n\n        case 'acosh':\n          // d/dx(acosh(x)) = 1 / sqrt(x^2 - 1); XXX potentially only for x >= 1 (the real spectrum)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])]);\n          break;\n\n        case 'atanh':\n          // d/dx(atanh(x)) = 1 / (1 - x^2)\n          div = true;\n          funcDerivative = new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])]);\n          break;\n\n        case 'asech':\n          // d/dx(asech(x)) = -1 / (x*sqrt(1 - x^2))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [arg0.clone(), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])])]);\n          break;\n\n        case 'acsch':\n          // d/dx(acsch(x)) = -1 / (|x|*sqrt(x^2 + 1))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acoth':\n          // d/dx(acoth(x)) = -1 / (1 - x^2)\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])]);\n          break;\n\n        case 'abs':\n          // d/dx(abs(x)) = abs(x)/x\n          funcDerivative = new OperatorNode('/', 'divide', [new FunctionNode(new SymbolNode('abs'), [arg0.clone()]), arg0.clone()]);\n          break;\n\n        case 'gamma': // Needs digamma function, d/dx(gamma(x)) = gamma(x)digamma(x)\n\n        default:\n          throw new Error('Function \"' + node.name + '\" is not supported by derivative, or a wrong number of arguments is passed');\n      }\n\n      var op, func;\n\n      if (div) {\n        op = '/';\n        func = 'divide';\n      } else {\n        op = '*';\n        func = 'multiply';\n      }\n      /* Apply chain rule to all functions:\n         F(x)  = f(g(x))\n         F'(x) = g'(x)*f'(g(x)) */\n\n\n      var chainDerivative = _derivative(arg0, constNodes);\n\n      if (negative) {\n        chainDerivative = new OperatorNode('-', 'unaryMinus', [chainDerivative]);\n      }\n\n      return new OperatorNode(op, func, [chainDerivative, funcDerivative]);\n    },\n    'OperatorNode, Object': function OperatorNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      if (node.op === '+') {\n        // d/dx(sum(f(x)) = sum(f'(x))\n        return new OperatorNode(node.op, node.fn, node.args.map(function (arg) {\n          return _derivative(arg, constNodes);\n        }));\n      }\n\n      if (node.op === '-') {\n        // d/dx(+/-f(x)) = +/-f'(x)\n        if (node.isUnary()) {\n          return new OperatorNode(node.op, node.fn, [_derivative(node.args[0], constNodes)]);\n        } // Linearity of differentiation, d/dx(f(x) +/- g(x)) = f'(x) +/- g'(x)\n\n\n        if (node.isBinary()) {\n          return new OperatorNode(node.op, node.fn, [_derivative(node.args[0], constNodes), _derivative(node.args[1], constNodes)]);\n        }\n      }\n\n      if (node.op === '*') {\n        // d/dx(c*f(x)) = c*f'(x)\n        var constantTerms = node.args.filter(function (arg) {\n          return constNodes[arg] !== undefined;\n        });\n\n        if (constantTerms.length > 0) {\n          var nonConstantTerms = node.args.filter(function (arg) {\n            return constNodes[arg] === undefined;\n          });\n          var nonConstantNode = nonConstantTerms.length === 1 ? nonConstantTerms[0] : new OperatorNode('*', 'multiply', nonConstantTerms);\n          var newArgs = constantTerms.concat(_derivative(nonConstantNode, constNodes));\n          return new OperatorNode('*', 'multiply', newArgs);\n        } // Product Rule, d/dx(f(x)*g(x)) = f'(x)*g(x) + f(x)*g'(x)\n\n\n        return new OperatorNode('+', 'add', node.args.map(function (argOuter) {\n          return new OperatorNode('*', 'multiply', node.args.map(function (argInner) {\n            return argInner === argOuter ? _derivative(argInner, constNodes) : argInner.clone();\n          }));\n        }));\n      }\n\n      if (node.op === '/' && node.isBinary()) {\n        var arg0 = node.args[0];\n        var arg1 = node.args[1]; // d/dx(f(x) / c) = f'(x) / c\n\n        if (constNodes[arg1] !== undefined) {\n          return new OperatorNode('/', 'divide', [_derivative(arg0, constNodes), arg1]);\n        } // Reciprocal Rule, d/dx(c / f(x)) = -c(f'(x)/f(x)^2)\n\n\n        if (constNodes[arg0] !== undefined) {\n          return new OperatorNode('*', 'multiply', [new OperatorNode('-', 'unaryMinus', [arg0]), new OperatorNode('/', 'divide', [_derivative(arg1, constNodes), new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])])]);\n        } // Quotient rule, d/dx(f(x) / g(x)) = (f'(x)g(x) - f(x)g'(x)) / g(x)^2\n\n\n        return new OperatorNode('/', 'divide', [new OperatorNode('-', 'subtract', [new OperatorNode('*', 'multiply', [_derivative(arg0, constNodes), arg1.clone()]), new OperatorNode('*', 'multiply', [arg0.clone(), _derivative(arg1, constNodes)])]), new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])]);\n      }\n\n      if (node.op === '^' && node.isBinary()) {\n        var _arg = node.args[0];\n        var _arg2 = node.args[1];\n\n        if (constNodes[_arg] !== undefined) {\n          // If is secretly constant; 0^f(x) = 1 (in JS), 1^f(x) = 1\n          if ((0, _is.isConstantNode)(_arg) && (isZero(_arg.value) || equal(_arg.value, 1))) {\n            return createConstantNode(0);\n          } // d/dx(c^f(x)) = c^f(x)*ln(c)*f'(x)\n\n\n          return new OperatorNode('*', 'multiply', [node, new OperatorNode('*', 'multiply', [new FunctionNode('log', [_arg.clone()]), _derivative(_arg2.clone(), constNodes)])]);\n        }\n\n        if (constNodes[_arg2] !== undefined) {\n          if ((0, _is.isConstantNode)(_arg2)) {\n            // If is secretly constant; f(x)^0 = 1 -> d/dx(1) = 0\n            if (isZero(_arg2.value)) {\n              return createConstantNode(0);\n            } // Ignore exponent; f(x)^1 = f(x)\n\n\n            if (equal(_arg2.value, 1)) {\n              return _derivative(_arg, constNodes);\n            }\n          } // Elementary Power Rule, d/dx(f(x)^c) = c*f'(x)*f(x)^(c-1)\n\n\n          var powMinusOne = new OperatorNode('^', 'pow', [_arg.clone(), new OperatorNode('-', 'subtract', [_arg2, createConstantNode(1)])]);\n          return new OperatorNode('*', 'multiply', [_arg2.clone(), new OperatorNode('*', 'multiply', [_derivative(_arg, constNodes), powMinusOne])]);\n        } // Functional Power Rule, d/dx(f^g) = f^g*[f'*(g/f) + g'ln(f)]\n\n\n        return new OperatorNode('*', 'multiply', [new OperatorNode('^', 'pow', 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{ isConstantNode, typeOf } from '../../utils/is';\nimport { factory } from '../../utils/factory';\nvar name = 'derivative';\nvar dependencies = ['typed', 'config', 'parse', 'simplify', 'equal', 'isZero', 'numeric', 'ConstantNode', 'FunctionNode', 'OperatorNode', 'ParenthesisNode', 'SymbolNode'];\nexport var createDerivative = /* #__PURE__ */factory(name, dependencies, function (_ref) {\n  var typed = _ref.typed,\n      config = _ref.config,\n      parse = _ref.parse,\n      simplify = _ref.simplify,\n      equal = _ref.equal,\n      isZero = _ref.isZero,\n      numeric = _ref.numeric,\n      ConstantNode = _ref.ConstantNode,\n      FunctionNode = _ref.FunctionNode,\n      OperatorNode = _ref.OperatorNode,\n      ParenthesisNode = _ref.ParenthesisNode,\n      SymbolNode = _ref.SymbolNode;\n\n  /**\n   * Takes the derivative of an expression expressed in parser Nodes.\n   * The derivative will be taken over the supplied variable in the\n   * second parameter. If there are multiple variables in the expression,\n   * it will return a partial derivative.\n   *\n   * This uses rules of differentiation which can be found here:\n   *\n   * - [Differentiation rules (Wikipedia)](https://en.wikipedia.org/wiki/Differentiation_rules)\n   *\n   * Syntax:\n   *\n   *     derivative(expr, variable)\n   *     derivative(expr, variable, options)\n   *\n   * Examples:\n   *\n   *     math.derivative('x^2', 'x')                     // Node {2 * x}\n   *     math.derivative('x^2', 'x', {simplify: false})  // Node {2 * 1 * x ^ (2 - 1)\n   *     math.derivative('sin(2x)', 'x'))                // Node {2 * cos(2 * x)}\n   *     math.derivative('2*x', 'x').evaluate()          // number 2\n   *     math.derivative('x^2', 'x').evaluate({x: 4})    // number 8\n   *     const f = math.parse('x^2')\n   *     const x = math.parse('x')\n   *     math.derivative(f, x)                           // Node {2 * x}\n   *\n   * See also:\n   *\n   *     simplify, parse, evaluate\n   *\n   * @param  {Node | string} expr           The expression to differentiate\n   * @param  {SymbolNode | string} variable The variable over which to differentiate\n   * @param  {{simplify: boolean}} [options]\n   *                         There is one option available, `simplify`, which\n   *                         is true by default. When false, output will not\n   *                         be simplified.\n   * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode}    The derivative of `expr`\n   */\n  var derivative = typed('derivative', {\n    'Node, SymbolNode, Object': function NodeSymbolNodeObject(expr, variable, options) {\n      var constNodes = {};\n      constTag(constNodes, expr, variable.name);\n\n      var res = _derivative(expr, constNodes);\n\n      return options.simplify ? simplify(res) : res;\n    },\n    'Node, SymbolNode': function NodeSymbolNode(expr, variable) {\n      return derivative(expr, variable, {\n        simplify: true\n      });\n    },\n    'string, SymbolNode': function stringSymbolNode(expr, variable) {\n      return derivative(parse(expr), variable);\n    },\n    'string, SymbolNode, Object': function stringSymbolNodeObject(expr, variable, options) {\n      return derivative(parse(expr), variable, options);\n    },\n    'string, string': function stringString(expr, variable) {\n      return derivative(parse(expr), parse(variable));\n    },\n    'string, string, Object': function stringStringObject(expr, variable, options) {\n      return derivative(parse(expr), parse(variable), options);\n    },\n    'Node, string': function NodeString(expr, variable) {\n      return derivative(expr, parse(variable));\n    },\n    'Node, string, Object': function NodeStringObject(expr, variable, options) {\n      return derivative(expr, parse(variable), options);\n    } // TODO: replace the 8 signatures above with 4 as soon as typed-function supports optional arguments\n\n    /* TODO: implement and test syntax with order of derivatives -> implement as an option {order: number}\n    'Node, SymbolNode, ConstantNode': function (expr, variable, {order}) {\n      let res = expr\n      for (let i = 0; i < order; i++) {\n        let constNodes = {}\n        constTag(constNodes, expr, variable.name)\n        res = _derivative(res, constNodes)\n      }\n      return res\n    }\n    */\n\n  });\n  derivative._simplify = true;\n\n  derivative.toTex = function (deriv) {\n    return _derivTex.apply(null, deriv.args);\n  }; // FIXME: move the toTex method of derivative to latex.js. Difficulty is that it relies on parse.\n  // NOTE: the optional \"order\" parameter here is currently unused\n\n\n  var _derivTex = typed('_derivTex', {\n    'Node, SymbolNode': function NodeSymbolNode(expr, x) {\n      if (isConstantNode(expr) && typeOf(expr.value) === 'string') {\n        return _derivTex(parse(expr.value).toString(), x.toString(), 1);\n      } else {\n        return _derivTex(expr.toString(), x.toString(), 1);\n      }\n    },\n    'Node, ConstantNode': function NodeConstantNode(expr, x) {\n      if (typeOf(x.value) === 'string') {\n        return _derivTex(expr, parse(x.value));\n      } else {\n        throw new Error(\"The second parameter to 'derivative' is a non-string constant\");\n      }\n    },\n    'Node, SymbolNode, ConstantNode': function NodeSymbolNodeConstantNode(expr, x, order) {\n      return _derivTex(expr.toString(), x.name, order.value);\n    },\n    'string, string, number': function stringStringNumber(expr, x, order) {\n      var d;\n\n      if (order === 1) {\n        d = '{d\\\\over d' + x + '}';\n      } else {\n        d = '{d^{' + order + '}\\\\over d' + x + '^{' + order + '}}';\n      }\n\n      return d + \"\\\\left[\".concat(expr, \"\\\\right]\");\n    }\n  });\n  /**\n   * Does a depth-first search on the expression tree to identify what Nodes\n   * are constants (e.g. 2 + 2), and stores the ones that are constants in\n   * constNodes. Classification is done as follows:\n   *\n   *   1. ConstantNodes are constants.\n   *   2. If there exists a SymbolNode, of which we are differentiating over,\n   *      in the subtree it is not constant.\n   *\n   * @param  {Object} constNodes  Holds the nodes that are constant\n   * @param  {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n   * @param  {string} varName     Variable that we are differentiating\n   * @return {boolean}  if node is constant\n   */\n  // TODO: can we rewrite constTag into a pure function?\n\n\n  var constTag = typed('constTag', {\n    'Object, ConstantNode, string': function ObjectConstantNodeString(constNodes, node) {\n      constNodes[node] = true;\n      return true;\n    },\n    'Object, SymbolNode, string': function ObjectSymbolNodeString(constNodes, node, varName) {\n      // Treat other variables like constants. For reasoning, see:\n      //   https://en.wikipedia.org/wiki/Partial_derivative\n      if (node.name !== varName) {\n        constNodes[node] = true;\n        return true;\n      }\n\n      return false;\n    },\n    'Object, ParenthesisNode, string': function ObjectParenthesisNodeString(constNodes, node, varName) {\n      return constTag(constNodes, node.content, varName);\n    },\n    'Object, FunctionAssignmentNode, string': function ObjectFunctionAssignmentNodeString(constNodes, node, varName) {\n      if (node.params.indexOf(varName) === -1) {\n        constNodes[node] = true;\n        return true;\n      }\n\n      return constTag(constNodes, node.expr, varName);\n    },\n    'Object, FunctionNode | OperatorNode, string': function ObjectFunctionNodeOperatorNodeString(constNodes, node, varName) {\n      if (node.args.length > 0) {\n        var isConst = constTag(constNodes, node.args[0], varName);\n\n        for (var i = 1; i < node.args.length; ++i) {\n          isConst = constTag(constNodes, node.args[i], varName) && isConst;\n        }\n\n        if (isConst) {\n          constNodes[node] = true;\n          return true;\n        }\n      }\n\n      return false;\n    }\n  });\n  /**\n   * Applies differentiation rules.\n   *\n   * @param  {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n   * @param  {Object} constNodes  Holds the nodes that are constant\n   * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode}    The derivative of `expr`\n   */\n\n  var _derivative = typed('_derivative', {\n    'ConstantNode, Object': function ConstantNodeObject(node) {\n      return createConstantNode(0);\n    },\n    'SymbolNode, Object': function SymbolNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      return createConstantNode(1);\n    },\n    'ParenthesisNode, Object': function ParenthesisNodeObject(node, constNodes) {\n      return new ParenthesisNode(_derivative(node.content, constNodes));\n    },\n    'FunctionAssignmentNode, Object': function FunctionAssignmentNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      return _derivative(node.expr, constNodes);\n    },\n    'FunctionNode, Object': function FunctionNodeObject(node, constNodes) {\n      if (node.args.length !== 1) {\n        funcArgsCheck(node);\n      }\n\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      var arg0 = node.args[0];\n      var arg1;\n      var div = false; // is output a fraction?\n\n      var negative = false; // is output negative?\n\n      var funcDerivative;\n\n      switch (node.name) {\n        case 'cbrt':\n          // d/dx(cbrt(x)) = 1 / (3x^(2/3))\n          div = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [createConstantNode(3), new OperatorNode('^', 'pow', [arg0, new OperatorNode('/', 'divide', [createConstantNode(2), createConstantNode(3)])])]);\n          break;\n\n        case 'sqrt':\n        case 'nthRoot':\n          // d/dx(sqrt(x)) = 1 / (2*sqrt(x))\n          if (node.args.length === 1) {\n            div = true;\n            funcDerivative = new OperatorNode('*', 'multiply', [createConstantNode(2), new FunctionNode('sqrt', [arg0])]);\n          } else if (node.args.length === 2) {\n            // Rearrange from nthRoot(x, a) -> x^(1/a)\n            arg1 = new OperatorNode('/', 'divide', [createConstantNode(1), node.args[1]]); // Is a variable?\n\n            constNodes[arg1] = constNodes[node.args[1]];\n            return _derivative(new OperatorNode('^', 'pow', [arg0, arg1]), constNodes);\n          }\n\n          break;\n\n        case 'log10':\n          arg1 = createConstantNode(10);\n\n        /* fall through! */\n\n        case 'log':\n          if (!arg1 && node.args.length === 1) {\n            // d/dx(log(x)) = 1 / x\n            funcDerivative = arg0.clone();\n            div = true;\n          } else if (node.args.length === 1 && arg1 || node.args.length === 2 && constNodes[node.args[1]] !== undefined) {\n            // d/dx(log(x, c)) = 1 / (x*ln(c))\n            funcDerivative = new OperatorNode('*', 'multiply', [arg0.clone(), new FunctionNode('log', [arg1 || node.args[1]])]);\n            div = true;\n          } else if (node.args.length === 2) {\n            // d/dx(log(f(x), g(x))) = d/dx(log(f(x)) / log(g(x)))\n            return _derivative(new OperatorNode('/', 'divide', [new FunctionNode('log', [arg0]), new FunctionNode('log', [node.args[1]])]), constNodes);\n          }\n\n          break;\n\n        case 'pow':\n          constNodes[arg1] = constNodes[node.args[1]]; // Pass to pow operator node parser\n\n          return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes);\n\n        case 'exp':\n          // d/dx(e^x) = e^x\n          funcDerivative = new FunctionNode('exp', [arg0.clone()]);\n          break;\n\n        case 'sin':\n          // d/dx(sin(x)) = cos(x)\n          funcDerivative = new FunctionNode('cos', [arg0.clone()]);\n          break;\n\n        case 'cos':\n          // d/dx(cos(x)) = -sin(x)\n          funcDerivative = new OperatorNode('-', 'unaryMinus', [new FunctionNode('sin', [arg0.clone()])]);\n          break;\n\n        case 'tan':\n          // d/dx(tan(x)) = sec(x)^2\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('sec', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'sec':\n          // d/dx(sec(x)) = sec(x)tan(x)\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('tan', [arg0.clone()])]);\n          break;\n\n        case 'csc':\n          // d/dx(csc(x)) = -csc(x)cot(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('cot', [arg0.clone()])]);\n          break;\n\n        case 'cot':\n          // d/dx(cot(x)) = -csc(x)^2\n          negative = true;\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('csc', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'asin':\n          // d/dx(asin(x)) = 1 / sqrt(1 - x^2)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])]);\n          break;\n\n        case 'acos':\n          // d/dx(acos(x)) = -1 / sqrt(1 - x^2)\n          div = true;\n          negative = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])]);\n          break;\n\n        case 'atan':\n          // d/dx(atan(x)) = 1 / (x^2 + 1)\n          div = true;\n          funcDerivative = new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)]);\n          break;\n\n        case 'asec':\n          // d/dx(asec(x)) = 1 / (|x|*sqrt(x^2 - 1))\n          div = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acsc':\n          // d/dx(acsc(x)) = -1 / (|x|*sqrt(x^2 - 1))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acot':\n          // d/dx(acot(x)) = -1 / (x^2 + 1)\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)]);\n          break;\n\n        case 'sinh':\n          // d/dx(sinh(x)) = cosh(x)\n          funcDerivative = new FunctionNode('cosh', [arg0.clone()]);\n          break;\n\n        case 'cosh':\n          // d/dx(cosh(x)) = sinh(x)\n          funcDerivative = new FunctionNode('sinh', [arg0.clone()]);\n          break;\n\n        case 'tanh':\n          // d/dx(tanh(x)) = sech(x)^2\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('sech', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'sech':\n          // d/dx(sech(x)) = -sech(x)tanh(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('tanh', [arg0.clone()])]);\n          break;\n\n        case 'csch':\n          // d/dx(csch(x)) = -csch(x)coth(x)\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [node, new FunctionNode('coth', [arg0.clone()])]);\n          break;\n\n        case 'coth':\n          // d/dx(coth(x)) = -csch(x)^2\n          negative = true;\n          funcDerivative = new OperatorNode('^', 'pow', [new FunctionNode('csch', [arg0.clone()]), createConstantNode(2)]);\n          break;\n\n        case 'asinh':\n          // d/dx(asinh(x)) = 1 / sqrt(x^2 + 1)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])]);\n          break;\n\n        case 'acosh':\n          // d/dx(acosh(x)) = 1 / sqrt(x^2 - 1); XXX potentially only for x >= 1 (the real spectrum)\n          div = true;\n          funcDerivative = new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])]);\n          break;\n\n        case 'atanh':\n          // d/dx(atanh(x)) = 1 / (1 - x^2)\n          div = true;\n          funcDerivative = new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])]);\n          break;\n\n        case 'asech':\n          // d/dx(asech(x)) = -1 / (x*sqrt(1 - x^2))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [arg0.clone(), new FunctionNode('sqrt', [new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])])])]);\n          break;\n\n        case 'acsch':\n          // d/dx(acsch(x)) = -1 / (|x|*sqrt(x^2 + 1))\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('*', 'multiply', [new FunctionNode('abs', [arg0.clone()]), new FunctionNode('sqrt', [new OperatorNode('+', 'add', [new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)]), createConstantNode(1)])])]);\n          break;\n\n        case 'acoth':\n          // d/dx(acoth(x)) = -1 / (1 - x^2)\n          div = true;\n          negative = true;\n          funcDerivative = new OperatorNode('-', 'subtract', [createConstantNode(1), new OperatorNode('^', 'pow', [arg0.clone(), createConstantNode(2)])]);\n          break;\n\n        case 'abs':\n          // d/dx(abs(x)) = abs(x)/x\n          funcDerivative = new OperatorNode('/', 'divide', [new FunctionNode(new SymbolNode('abs'), [arg0.clone()]), arg0.clone()]);\n          break;\n\n        case 'gamma': // Needs digamma function, d/dx(gamma(x)) = gamma(x)digamma(x)\n\n        default:\n          throw new Error('Function \"' + node.name + '\" is not supported by derivative, or a wrong number of arguments is passed');\n      }\n\n      var op, func;\n\n      if (div) {\n        op = '/';\n        func = 'divide';\n      } else {\n        op = '*';\n        func = 'multiply';\n      }\n      /* Apply chain rule to all functions:\n         F(x)  = f(g(x))\n         F'(x) = g'(x)*f'(g(x)) */\n\n\n      var chainDerivative = _derivative(arg0, constNodes);\n\n      if (negative) {\n        chainDerivative = new OperatorNode('-', 'unaryMinus', [chainDerivative]);\n      }\n\n      return new OperatorNode(op, func, [chainDerivative, funcDerivative]);\n    },\n    'OperatorNode, Object': function OperatorNodeObject(node, constNodes) {\n      if (constNodes[node] !== undefined) {\n        return createConstantNode(0);\n      }\n\n      if (node.op === '+') {\n        // d/dx(sum(f(x)) = sum(f'(x))\n        return new OperatorNode(node.op, node.fn, node.args.map(function (arg) {\n          return _derivative(arg, constNodes);\n        }));\n      }\n\n      if (node.op === '-') {\n        // d/dx(+/-f(x)) = +/-f'(x)\n        if (node.isUnary()) {\n          return new OperatorNode(node.op, node.fn, [_derivative(node.args[0], constNodes)]);\n        } // Linearity of differentiation, d/dx(f(x) +/- g(x)) = f'(x) +/- g'(x)\n\n\n        if (node.isBinary()) {\n          return new OperatorNode(node.op, node.fn, [_derivative(node.args[0], constNodes), _derivative(node.args[1], constNodes)]);\n        }\n      }\n\n      if (node.op === '*') {\n        // d/dx(c*f(x)) = c*f'(x)\n        var constantTerms = node.args.filter(function (arg) {\n          return constNodes[arg] !== undefined;\n        });\n\n        if (constantTerms.length > 0) {\n          var nonConstantTerms = node.args.filter(function (arg) {\n            return constNodes[arg] === undefined;\n          });\n          var nonConstantNode = nonConstantTerms.length === 1 ? nonConstantTerms[0] : new OperatorNode('*', 'multiply', nonConstantTerms);\n          var newArgs = constantTerms.concat(_derivative(nonConstantNode, constNodes));\n          return new OperatorNode('*', 'multiply', newArgs);\n        } // Product Rule, d/dx(f(x)*g(x)) = f'(x)*g(x) + f(x)*g'(x)\n\n\n        return new OperatorNode('+', 'add', node.args.map(function (argOuter) {\n          return new OperatorNode('*', 'multiply', node.args.map(function (argInner) {\n            return argInner === argOuter ? _derivative(argInner, constNodes) : argInner.clone();\n          }));\n        }));\n      }\n\n      if (node.op === '/' && node.isBinary()) {\n        var arg0 = node.args[0];\n        var arg1 = node.args[1]; // d/dx(f(x) / c) = f'(x) / c\n\n        if (constNodes[arg1] !== undefined) {\n          return new OperatorNode('/', 'divide', [_derivative(arg0, constNodes), arg1]);\n        } // Reciprocal Rule, d/dx(c / f(x)) = -c(f'(x)/f(x)^2)\n\n\n        if (constNodes[arg0] !== undefined) {\n          return new OperatorNode('*', 'multiply', [new OperatorNode('-', 'unaryMinus', [arg0]), new OperatorNode('/', 'divide', [_derivative(arg1, constNodes), new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])])]);\n        } // Quotient rule, d/dx(f(x) / g(x)) = (f'(x)g(x) - f(x)g'(x)) / g(x)^2\n\n\n        return new OperatorNode('/', 'divide', [new OperatorNode('-', 'subtract', [new OperatorNode('*', 'multiply', [_derivative(arg0, constNodes), arg1.clone()]), new OperatorNode('*', 'multiply', [arg0.clone(), _derivative(arg1, constNodes)])]), new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])]);\n      }\n\n      if (node.op === '^' && node.isBinary()) {\n        var _arg = node.args[0];\n        var _arg2 = node.args[1];\n\n        if (constNodes[_arg] !== undefined) {\n          // If is secretly constant; 0^f(x) = 1 (in JS), 1^f(x) = 1\n          if (isConstantNode(_arg) && (isZero(_arg.value) || equal(_arg.value, 1))) {\n            return createConstantNode(0);\n          } // d/dx(c^f(x)) = c^f(x)*ln(c)*f'(x)\n\n\n          return new OperatorNode('*', 'multiply', [node, new OperatorNode('*', 'multiply', [new FunctionNode('log', [_arg.clone()]), _derivative(_arg2.clone(), constNodes)])]);\n        }\n\n        if (constNodes[_arg2] !== undefined) {\n          if (isConstantNode(_arg2)) {\n            // If is secretly constant; f(x)^0 = 1 -> d/dx(1) = 0\n            if (isZero(_arg2.value)) {\n              return createConstantNode(0);\n            } // Ignore exponent; f(x)^1 = f(x)\n\n\n            if (equal(_arg2.value, 1)) {\n              return _derivative(_arg, constNodes);\n            }\n          } // Elementary Power Rule, d/dx(f(x)^c) = c*f'(x)*f(x)^(c-1)\n\n\n          var powMinusOne = new OperatorNode('^', 'pow', [_arg.clone(), new OperatorNode('-', 'subtract', [_arg2, createConstantNode(1)])]);\n          return new OperatorNode('*', 'multiply', [_arg2.clone(), new OperatorNode('*', 'multiply', [_derivative(_arg, constNodes), powMinusOne])]);\n        } // Functional Power Rule, d/dx(f^g) = f^g*[f'*(g/f) + g'ln(f)]\n\n\n        return new OperatorNode('*', 'multiply', [new OperatorNode('^', 'pow', [_arg.clone(), _arg2.clone()]), new OperatorNode('+', 'add', [new OperatorNode('*', 'multiply', [_derivative(_arg, constNodes), new OperatorNode('/', 'divide', [_arg2.clone(), _arg.clone()])]), new OperatorNode('*', 'multiply', [_derivative(_arg2, constNodes), new FunctionNode('log', [_arg.clone()])])])]);\n      }\n\n      throw new Error('Operator \"' + node.op + '\" is not supported by derivative, or a wrong number of arguments is passed');\n    }\n  });\n  /**\n   * Ensures the number of arguments for a function are correct,\n   * and will throw an error otherwise.\n   *\n   * @param {FunctionNode} node\n   */\n\n\n  function funcArgsCheck(node) {\n    // TODO add min, max etc\n    if ((node.name === 'log' || node.name === 'nthRoot' || node.name === 'pow') && node.args.length === 2) {\n      return;\n    } // There should be an incorrect number of arguments if we reach here\n    // Change all args to constants to avoid unidentified\n    // symbol error when compiling function\n\n\n    for (var i = 0; i < node.args.length; ++i) {\n      node.args[i] = createConstantNode(0);\n    }\n\n    node.compile().evaluate();\n    throw new Error('Expected TypeError, but none found');\n  }\n  /**\n   * Helper function to create a constant node with a specific type\n   * (number, BigNumber, Fraction)\n   * @param {number} value\n   * @param {string} [valueType]\n   * @return {ConstantNode}\n   */\n\n\n  function createConstantNode(value, valueType) {\n    return new ConstantNode(numeric(value, valueType || config.number));\n  }\n\n  return derivative;\n});"},"lineCount":null}},"error":null,"hash":"3ee44284d53119c8b027165b32aada31","cacheData":{"env":{}}}