Answer
$y'=2x \cot(5x)-5x^2 csc^2(5x)$
Work Step by Step
Given that $y=x^2 \cot 5x$
Apply derivative rules of differentiation:
$f(x)=p'(x)q(x)+p(x)q'(x)$
$y'=\dfrac{d}{dx}[x^2 \cot 5x]$
$=2x \cot 5x-x^2 csc^2(5x) \dfrac{d}{dx}[5x]$
$=2x \cot(5x)-5x^2 csc^2(5x)$
Hence, $y'=2x \cot(5x)-5x^2 csc^2(5x)$
