Define the derivative of a function f(x) and use this to calculate the derivative of f(x)=x^n for positive integer n.

f'(x)=lim(h->0) of [f(x+h)-f(x)]/h. In the case where f(x)=x^n, we have that f(x+h)-f(x)=h*nx^(n-1) + (h^2)*p(x) for a polynomial p(x), shown by binomially expanding f(x+h). Then dividing through by h and taking the limit gives f'(x)=nx^n-1.