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Math Help - differentiation tan -1 and ln (e^x)

  1. #1
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    differentiation tan -1 and ln (e^x)

    Hi

    I need to differentiate the function g(x) = tan ^-1 (x^(1/2))/ ln (e^x)

    I am assuming I will use the quotient rule so

    g'(x) = ln (e^x) X (1/(1+x^2))(1/2x^-1/2) dx - tan ^-1(x^(1/2)) e^x dx

    it says not to simplify so am I right or am completely off track?

    Thanks

    Calculus Beginner
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  2. #2
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    Are you sure the problem says \ln e^x? Because \ln e^x=x, the derivative simplifies to

    \frac{d}{dx}\tan^{-1}\sqrt{x}.

    Now we may use the Chain Rule together with the fact that

    \frac{d}{dx}\tan^{-1}x=\frac{1}{1+x^2}.
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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Scott H View Post
    ... are you sure the problem says \ln e^x? Because \ln e^x=x, the derivative simplifies...
    ... may be that someone at this point horns in on and says something like that: you are wrongh!... everibody with a minimum of mathematical background knows that is...

    e^{\ln x} = x + 2\pi k i

    ... some people are funny! ... no problem! ...

    Kind regards

    \chi \sigma
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  4. #4
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    Well, conventionally we use z to denote complex numbers...
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