Proof by induction is a method in which one begins by showing that a statement, which involves positive integers, is true for a particular value (usually k = 1). In the second step, the statement is assumed to be true for k = n, and the statement is proved for k = n + 1, which concludes the proof.

a. Show that d/dx (e^kx) = ke^kx, for k = 1.

b. Assume the rule is true for k = n (that is, assume d/dx (e^nx) = ne^nx), and show this assumption implies that the rule is true for k = n + 1. Write e^{(n + 1)} as the product of two functions and use the Product Rule.)