Assuming that the power rule is true for n, find d(xn+1)/dx using the product rule, and check

Question:

Assuming that the power rule is true for n, find d(xn+1)/dx using the product rule, and check that it too satisfies the power rule.
For positive integer powers, it is possible to derive the power rule with mathematical induction. The idea is to show that a formula is true for n = l, and then that if it is true for some particular n, it must then also be true for n + 1.