What is (\partial)/(\partial x)(e^{-(x+y)}) ?

The answer to (\partial)/(\partial x)(e^{-(x+y)}) is -e^{-x-y}

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(\partial)/(\partial x)(e^{-(x+y)})

\frac{\partial}{\partial x} (e^{- (x + y)})

- e^{- x - y}

Solution steps

\frac{\partial}{\partial x} (e^{- (x + y)})

Simplify

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

= \frac{\partial}{\partial x} (e^{- x - y})

Treat

y

as a constant

Apply the chain rule:

e^{- x - y} \frac{\partial}{\partial x} (- x - y)

= e^{- x - y} \frac{\partial}{\partial x} (- x - y)

\frac{\partial}{\partial x} (- x - y) = - 1

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

Simplify

= - e^{- x - y}

What is (\partial)/(\partial x)(e^{-(x+y)}) ?
The answer to (\partial)/(\partial x)(e^{-(x+y)}) is -e^{-x-y}