Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 151: 10

$f'(x)=-\sin x-\csc x+x\cot x\csc x$

$f(x)=cosx-xcscx$ $f'(x)=-sinx-(\frac{d}{dx}(x)\times{cscx}+x\times{\frac{d}{dx}(cscx)}$ $f'(x)=-sinx-(1\times{cscx}+x\times{-cotxcscx})$ $f'(x)=-sinx-(cscx-xcotxcscx)$ $f'(x)=-\sin x-\csc x+x\cot x\csc x$