Difference between revisions of "Power rule"
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| − | + | 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 | |
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| + | <math> \frac{d}{dx} (x^n) = nx^{n-1} </math> | ||
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| + | 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 | ||
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| + | <math> f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x) </math> | ||
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[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 05:16, December 16, 2009
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>