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Math Help - Math Induction derivative help

  1. #1
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    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
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  2. #2
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    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?
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