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Power rule

The power rule is used to calculate the derivative of a power function. If n is a positive integer, then

 


Explanation

We start with the function

Substitution in the definition of the derivative gives

We now use the formula for the division

with a = x + Δx and b = x and thus a – b = Δx. Substitution gives

The limit of a sum is the sum of the limits, so

There are n terms, so

 


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