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Math Help - plz help inverse derivative

  1. #1
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    plz help inverse derivative

    Let f(x)= 2x+ln(x).and let g be the inverse function of f.Find the value of g ' (2)
    (a)1 (b)1/2 (c)1/3 (d)1/ln(2) (e)1/2ln(2) (f)none
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gracy View Post
    Let f(x)= 2x+ln(x).and let g be the inverse function of f.Find the value of g ' (2)
    (a)1 (b)1/2 (c)1/3 (d)1/ln(2) (e)1/2ln(2) (f)none
    The point at which f(x)=2, is x=1.

    We have:

    g(f(x))=x,

    so:

    g(2x+ln(x))=x

    hence:

    (2+1/x)g'(2x+ln(x))=1.

    So put x=1, then g'(2)=1/3.

    RonL
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