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Math Help - Differentiation

  1. #1
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    Differentiation

    Differentiate:
    {\frac{1-xe^x}{x+e^x}}

    I'm new to this stuff and this one seems to be a bit tricky. If you could please break it down step by step that would be very helpful.
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  2. #2
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    Quote Originally Posted by Neversh View Post
    Differentiate:
    {\frac{1-xe^x}{x+e^x}}

    I'm new to this stuff and this one seems to be a bit tricky. If you could please break it down step by step that would be very helpful.
    Use the Quotient Rule

    \frac{dy}{dx} = \frac{(x + e^x)\frac{d}{dx}(1 - xe^x) - (1 - xe^x)\frac{d}{dx}(x + e^x)}{(x + e^x)^2}

     = \frac{(x + e^x)(-e^x - xe^x) - (1 - xe^x)(1 + e^x)}{(x + e^x)^2}

     = \frac{-e^x(x + e^x)(1 + x) - (1 - xe^x)(1 + e^x)}{(x + e^x)^2}
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