Derivative of Arcsine of Function

Theorem
Let $u$ be a differentiable real function of $x$ such that $\size {\map u x} < 1$, that is, $\size {\arcsin u} < \dfrac \pi 2$.

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

where $\arcsin$ denotes the real arcsine of $x$.

Also see

 * Derivative of Arccosine of Function
 * Derivative of Arctangent of Function
 * Derivative of Arccotangent of Function
 * Derivative of Arcsecant of Function
 * Derivative of Arccosecant of Function