\underset{By definition of v_{1}}{\underset{︸}{u_{1} (x, z_{1}) = v_{1} + {\dot{u}}_{x}}} = \overset{v_{1}}{\overset{︷}{- \frac{\partial V_{x}}{\partial x} g_{x} (x) - k_{1} (\underset{e_{1}}{\underset{︸}{z_{1} - u_{x} (x)}})}} + \overset{{\dot{u}}_{x} (i.e., \frac{d}{u_{x}})}{\overset{︷}{\frac{\partial u_{x}}{\partial x} (\underset{\dot{x} (i.e., \frac{d}{x})}{\underset{︸}{f_{x} (x) + g_{x} (x) z_{1}}})}}