Answer
$y'=cos^{-1}(x)-\frac{x}{\sqrt{1-x^2}}$
Work Step by Step
Start with the function $y=xcos^{-1}(x)$.
Use the product rule and inverse cosine rules to differentiate: $y'=1*cos^{-1}(x)+x*(-\frac{1}{\sqrt{1-x^2}})$.
Simplify to arrive at answer: $y'=cos^{-1}(x)-\frac{x}{\sqrt{1-x^2}}$.
