You assume that p(k) is true which means
You want to show that p(k+1) is true :
Just take the derivative of
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.