How do you find the derivative of $\frac{1}{x^2}$?

Solve for the derivative:

As we know that $\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$

So,

$\begin{array}{rcl}\frac{d}{dx}\left(\frac{1}{x^2}\right)& =& \frac{d}{dx}\left(x^{-2}\right)\\ & =& -2{\left(x\right)}^{-2-1}\\ & =& -2{\left(x\right)}^{-3}\\ & =& \frac{-2}{x^3}\end{array}$

Hence, the derivative of $\frac{1}{x^2}$is $\frac{-2}{x^3}$.