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Math Help - Multi-variable Derivative of e raised to a negative power

  1. #1
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    Multi-variable Derivative of e raised to a negative power

    I have,

    e^-(x+y)
    I need to find what the derivative is with respect to Y. My answer I found was simply the same as above and I didn't seem to think it was correct.
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  2. #2
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    e^{-(x+y)} can be rewritten as e^{-x-y}=e^{-x}e^{-y} so if you treat e^{-x} as a constant then you just have to differentiate \frac{\partial}{\partial y} e^{-x}e^{-y} =-e^{-x}e^{-y}<br />
=-e^{-x-y}=-e^{-(x+y)}

    so your final solution should be:

    -e^{-(x+y)}
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