What is (\partial)/(\partial y)(x^2e^{-y}) ?

The answer to (\partial)/(\partial y)(x^2e^{-y}) is -e^{-y}x^2

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(\partial)/(\partial y)(x^2e^{-y})

\frac{\partial}{\partial y} (x^{2} e^{- y})

- e^{- y} x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{2} e^{- y})

Treat

x

as a constant

Take the constant out:

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

= x^{2} \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^{2} e^{- y} (- 1)

Simplify

= - e^{- y} x^{2}

x \to 0 lim ((1 - x)^{\frac{1}{x}})

\frac{d}{d t} (- s t)

(u^{- 2} + u^{- 3}) (u^{5} - 4 u^{2})

y^{^{'}} = (\frac{y + 3}{4 x + 5})^{3}

\frac{2 x}{7 - cot ( x )}

What is (\partial)/(\partial y)(x^2e^{-y}) ?
The answer to (\partial)/(\partial y)(x^2e^{-y}) is -e^{-y}x^2