Proof by induction: derivative of ekx for positive integers k Proof by induction is a meth...

Proof by induction: derivative of ekx for positive integers k 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 , for k = 1.

b. Assume the rule is true for k = n (that is, assume , and show this assumption implies that the rule is true for k = n + 1. (Hint: Write e(n + 1)x as the product of two functions and use the Product Rule.)