Multi-variable Derivative of e raised to a negative power

**Iceman75x** · February 24th 2009, 07:05 PM

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.

**lllll** · February 24th 2009, 08:57 PM

$e^{-(x+y)}$ 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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