#### Answer

$y'=-10x \csc^2 x^2$

#### Work Step by Step

Given that $y=5 \cot x^2$
Apply derivative rules of differentiation:
$f(x)=p'(x)q(x)+p(x)q'(x)$
$y'=\dfrac{d}{dx}[5 \cot x^2]$
$=-5 \csc^2 x^2 \dfrac{d}{dx}[x^2]$
$=-5 \csc^2 x^2 (2x)$
Hence, $y'=-10x \csc^2 x^2$