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Math Help - if f(x) = e^2x and g(x) =lnx, then the derivative of...

  1. #1
    Junior Member LexiRae's Avatar
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    if f(x) = e^2x and g(x) =lnx, then the derivative of...

    if f(x) = e^2x and g(x) =lnx, then the derivative of y = f(g(x)) at x=e is?

    no idea how to do this!
    thanks in advance!
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  2. #2
    Junior Member
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    Quote Originally Posted by LexiRae View Post
    if f(x) = e^2x and g(x) =lnx, then the derivative of y = f(g(x)) at x=e is?

    no idea how to do this!
    thanks in advance!
    One way of doing it is substituting you get

    f(g(x)) = \exp(2*\ln(x))

     = \exp(\ln(x^2))

     = x^2

    Then the derivative

    (f(g(x))' = 2x

    So at x = e

    (f(g(x))' = 2e


    HTH
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