Derivative of Composite Function/Examples/Root of Arcsine of x

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\sqrt {\arcsin x} } = \dfrac 1 {2 \sqrt {\paren {1 - x^2} \arcsin x } }$

Proof
Let $u = \arcsin x$.

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

Thus we have:
 * $y = \paren {\arcsin x}^{1/2}$

and so: