#### Answer

The Derivative is:
$y'=-x^2\csc^2 x+2x\cot x+\frac{2}{x^3}$

#### Work Step by Step

$y=x^2\cot x-\frac{1}{x^2}$
Applying Derivative Rules:
$y'=f'(x)+g'(x)$ and $f'(x)=h'(x)\cdot r(x)+h(x)\cdot r'(x)$
$y'=[((2)x^{2-1})(\cot x)+(x^2)(-\csc^2 x)] - (-2)x^{-2-1}$
$y'=2x\cot x-x^2\csc^2 x+\frac{2}{x^3}$
$y'=-x^2\csc^2 x+2x\cot x+\frac{2}{x^3}$