Find the derivative of arccos (1-x²)^1/2

by RoRi

November 29, 2015

Find the derivative of the function

$f(x) = \arccos \sqrt{1-x^2}.$

To compute the derivative we use the chain rule and the formula for the derivative of arccosine,

$\begin{align*} f'(x) &= \left(\frac{-x}{\sqrt{1-x^2}}\right) \left(\frac{-1}{\sqrt{1-1+x^2}} \right) \\ &= \frac{x}{|x| \sqrt{1-x^2}}. \end{align*}$

This formula is valid for $0 < |x| < 1$ .

Stumbling Robot