Derivative of Composite Function/Examples/Root of sin x

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\sqrt {\sin x} } = \dfrac {\cos x} {2 \sqrt {\sin x} }$

Proof
Let $u = \sin x$.

Let $y = u^{1/2}$.

Thus by definition of square root we have:
 * $y = \paren {\sin x}^{1/2}$

and so: