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A power rule is any mathematical rule or shortcut that applies when there is a variable to a constant power. The most common example is the power rule of differentiation, f'(xⁿ)=nx^n-1

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>

 

for all integers <math> n </math>.  This rule is useful when combined with the [[chain rule]].  As an example we can compute the derivative of <math> f(x) = (\sin(x))^n</math> as

 

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

 

[[Category:Mathematics]]

[[Category:Mathematics]]