Find the derivative of arcsin (x/2)

by RoRi

November 29, 2015

Find the derivative of the function

$f(x) = \arcsin \frac{x}{2}.$

Using the chain rule and the derivative of arcsine we have

$f'(x) = \left( \frac{1}{2} \right) \left( \frac{1}{\sqrt{1- \left(\frac{x}{2}\right)^2}} \right) = \frac{1}{\sqrt{4-x^2}}.$

This is valid for $|x| < 2$ (since the domain of $\arcsin x$ is $|x| < 1$ ).

Stumbling Robot