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})

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}

\frac{\partial}{\partial y} (x^{2} y z^{2} + sin (yz))

\frac{d x}{d t} = x - x^{2}

\frac{d}{d x} (4^{3 x})

\int \frac{6 x + 4}{x ^{2} ( x ^{2} + 2 )} d x

(x - 2 y) d y + (y + 4 x) d x = 0

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