Differentiate power functions

For a power function $f(x)=x^n$, differentiation gives $f'(x)=nx^{n-1}$, so the derivative represents the instantaneous rate of change or tangent slope and can be used with constant multiples and sums of power terms. The rule applies to standard integer powers, including zero and negative powers where the function is defined, with simple rational powers when included in the introductory domain; generalized real or complex exponents are not included.