Derivative of Arccosine of Function

Theorem
Let $u$ be a differentiable real function of $x$ such that $\size {\map u x} < 1$, that is, $0 < \arccos u < \pi$.

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

where $\arccos$ denotes the arccosine of $x$.

Also see

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