Calculus: Early Transcendentals 8th Edition

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