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

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

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(\partial)/(\partial y)(xe^{-y})

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

- e^{- y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= - e^{- y} x

y = x^{3} + e^{x}

y^{^{''}} - 4 y^{^{'}} + 5 y = 1 + 5 x

\int 9 x + 6 d x

\int \frac{x}{x ^{4} + 3 x ^{2} - 4} d x

n = 1 \sum \infty \frac{n + 2}{n !}

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