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

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

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

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

- e^{- x - y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= - e^{- x - y}

f (x) = 7 x + 1, at x = 9

n = 0 \sum \infty \frac{3}{n ( n + 3 )}

\int \frac{2 x + 1}{x ^{6} + 18 x ^{4} + 81 x ^{2}} d x

n = 1 \sum \infty \frac{5}{n ^{2} + 9 n + 7}

x \to \frac{π}{2} lim (x sin (x))

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