Power Rule

Power Rule - Intuition

• $\frac{df}{dx}=\frac{\text{amount of change in output}}{\text{amount of change in input}}$
• $\frac{df}{dx}=\frac{f(x+dx)-f(x)}{dx}$
• $\frac{df}{dx}=\frac{(x+dx{)}^2-x^2}{dx}$
• $\frac{df}{dx}=\frac{x^2+2xdx+d{x}^2-x^2}{dx}$
• $\frac{df}{dx}=\frac{2xdx+d{x}^2}{dx}$
• $\frac{df}{dx}=2x+dx$
• $\frac{df}{dx}=2x$