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Math Help - Differentiate a function

  1. #1
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    Differentiate a function

    Hello guys,

    Having trouble with differentiating this function, hope you could help me.

    y = (e^(-x))(1 - e^(2x))

    y = (e^-x)(1 - e^(2x))

    I tried expanding the bracket first, but then my answer doesn't agree with many diff calculators.

    thanks again.
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  2. #2
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    Method 1: Expand brackets first

    y = e^{-x}(1 - e^{2x})

     = e^{-x} - e^{x}

    so \displaystyle{\frac{dy}{dx} = -e^{-x} - e^{x}}.


    Method 2: Use the Product Rule.

    y = e^{-x}(1 - e^{2x})

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

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

     = -2e^x - e^{-x} + e^x

     = -e^{-x} - e^x.
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  3. #3
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    Ahhh, thats the answer I had! Those dammed calculators.

    Thanks again for your time.
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