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Math Help - Derivative question involving both e and ln

  1. #1
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    Derivative question involving both e and ln

    y = e^(-x) * ln x

    I'm stumped on how to proceed here. Up until now I've only derived problems concerning ln alone. A step by step solution would be very much appreciated.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Archduke01 View Post
    y = e^(-x) * ln x

    I'm stumped on how to proceed here. Up until now I've only derived problems concerning ln alone. A step by step solution would be very much appreciated.
    Are you familiar with the product rule?

    \left(fg\right)^{\prime}=f^{\prime}g+g^{\prime}f.

    In your case, let f(x)=e^{-x} and g(x)=\ln x.

    Can you try to take it from here?
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Archduke01 View Post
    y = e^(-x) * ln x

    I'm stumped on how to proceed here. Up until now I've only derived problems concerning ln alone. A step by step solution would be very much appreciated.
    \frac{d}{dx}[e^{-x}\ln{x}]=e^{-x}\left(\frac{1}{x}\right)+(-e^{-x})\ln{x}

    This is the solution. The product rule is what was needed.
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