Prove by induction the nth derivative of e^(a*x) is (a^n)*e^(a*x) for all n that exist in the natural numbers greater than or equal to 1.

That was the conjecture I made from the taking a few derivatives.

After showing p(1) is true and assuming p(k) is true, how do I start proving p(k+1) is true.

I thought about starting with p(k) and multiplying by a but I don't think that will work in this situation since the derivative must be taking.