Changes

The power rule allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself.  The power rule states that

The '''power rule''' allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself.  The power rule states that

<math> \frac{d}{dx} (x^n) = nx^{n-1} </math>

<math> \frac{d}{dx} (x^n) = nx^{n-1} </math>

<math> f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x) </math>

<math> f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x) </math>

===Proof===

==Proof==

The power rule is simple and elegant to prove with the definition of a derivative:

The power rule is simple and elegant to prove with the definition of a derivative: