one may take differential forms of degrees k and l, denoted , with the wedge or exterior product operation , as well as the exterior derivative . Then one has the graded Leibniz rule: Applications Among the applications of the product rule is a proof that when n is a positive integer (this rule is true even if n is not positive or is not an integer, but the proof of that must rely on other methods). The proof is by mathematical induction on the exponent n. If n = 0 then xn is constant and nxn − 1 = 0. The rule holds in that case because the derivative of a constant function is 0. If the rule holds for any particular exponent n, then for the next value, n + 1, we have Therefore, if the proposition is true for n, it is true also for n + 1, and therefore for all natural n. See also References Articles containing proofs Differentiation rules Theorems in analysis Theorems in calculus