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