Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 26

$$y' =\cos^{-1} \left(x\right)-\frac{x}{\sqrt{1-x^2}}$$

Given $$y=x\cos^{-1}x$$ Then \begin{align*} y'&=\frac{d}{dx}\left(x\right)\cos^{-1} \left(x\right)+\frac{d}{dx}\left(\cos^{-1} \left(x\right)\right)x\\ &=\cos^{-1} \left(x\right)-\frac{x}{\sqrt{1-x^2}} \end{align*}