# Math Induction derivative help

• April 12th 2013, 12:46 PM
Hidee
Math Induction derivative help
Hi, if anybody can help me with this question, it would be greatly appreciated :)

Use mathematical induction to prove that fn(x) = (2nx+ n2n-1) e2x where fn(x) represents the nth derivative of f(x)

f(x) = xe2x
• April 12th 2013, 12:59 PM
HallsofIvy
Re: Math Induction derivative help
Well, obviously when n= 1, $f'(x)= e^{2x}+ 2xe^{2x}= (2x+ 1)e^{2x}= (2^1x+ 2^0)e^{2x}$.

Now, assume it is true for n= k: $f^k(x)= (2^k+ k^{k-2}})e^{2x}$
What is the derivative of that?