I have posted about induction on it's own so I think I understand that part. But I'm slightly confused when it comes to using induction to show that $n+1$ is also the derivative. The base case if fine, I just set $n=1$. And show that is equal to the derivative not using the formula. But how about $k+1$? Can I just choose $k=$the-basecase. And than prove $k+1$ by just finding $f''(x)$?
$f^{(n)}(x) = a^{n-1}e^{ax}(ax+n)$