### 11 - Demonstarting Power Rule in Examples

Here are some examples to show how the power rule for differentiation is used to find the derivative of some power functions.

Example 1. Let $y={x}^{4}$  , then $\frac{dy}{dx}=4{x}^{4-1}=4{x}^{3}$.

Example 2. Let $y={x}^{3.6}$  , then $\frac{dy}{dx}=3.6{x}^{3.6-1}=3.6{x}^{2.6}$.

Example 3. Let $y={x}^{-5}$ , then $\frac{dy}{dx}=-5{x}^{-5-1}=-5{x}^{-6}$.

Example 4. Let $y={x}^{\sqrt{2}}$  , then $\frac{dy}{dx}=\sqrt{2}{x}^{\sqrt{2}-1}$

Example 5. Let $y={x}^{\frac{2}{3}}$  , then $\frac{dy}{dx}=\frac{2}{3}{x}^{\frac{2}{3}-1}=\frac{2}{3}{x}^{\frac{-1}{3}}$

Example 6. Let $y={x}^{\pi }$  , then $\frac{dy}{dx}=\pi {x}^{\pi -1}$

Example 7. Let $y=\frac{1}{{x}^{5}}={x}^{-5}$  , then $\frac{dy}{dx}=-5{x}^{-5-1}=-5{x}^{-6}=\frac{-5}{{x}^{6}}$