Hi, if anybody can help me with this question, it would be greatly appreciated :)

Use mathematical induction to prove that f^{n}(x) = (2^{n}x+ n2^{n-1}) e^{2x}where f^{n}(x) represents the nth derivative of f(x)

f(x) = xe^{2x}

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- Apr 12th 2013, 11:46 AMHideeMath Induction derivative help
Hi, if anybody can help me with this question, it would be greatly appreciated :)

Use mathematical induction to prove that f^{n}(x) = (2^{n}x+ n2^{n-1}) e^{2x}where f^{n}(x) represents the nth derivative of f(x)

f(x) = xe^{2x} - Apr 12th 2013, 11:59 AMHallsofIvyRe: Math Induction derivative help
Well, obviously when n= 1, $\displaystyle f'(x)= e^{2x}+ 2xe^{2x}= (2x+ 1)e^{2x}= (2^1x+ 2^0)e^{2x}$.

Now, assume it is true for n= k: $\displaystyle f^k(x)= (2^k+ k^{k-2}})e^{2x}$

What is the derivative of that?