Answer
See explanations.
Work Step by Step
Step 1. Recall the Derivative Quotient Rule: $\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$
Step 2. Let $u=1$, we have: $\frac{d}{dx}(\frac{1}{v})=\frac{0-\frac{dv}{dx}}{v^2}=-\frac{1}{v^2}(\frac{dv}{dx})$
Step 3. Let $v=x^m$, we have $\frac{d}{dx}(x^{-m})=\frac{d}{dx}(\frac{1}{x^m})=-\frac{1}{(x^m)^2}(\frac{dx^m}{dx})=-\frac{mx^{m-1}}{(x^m)^2}=-mx^{m-1-2m}=-mx^{-m-1}$ which gives the Power Rule for negative integers.
