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

The answer to (\partial)/(\partial y)(xe^{-x^2y}) is -e^{-x^2y}x^3

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

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

- e^{- x^{2} y} x^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

x e^{- x^{2} y} (- x^{2}) : - e^{- x^{2} y} x^{3}

= - e^{- x^{2} y} x^{3}

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What is (\partial)/(\partial y)(xe^{-x^2y}) ?
The answer to (\partial)/(\partial y)(xe^{-x^2y}) is -e^{-x^2y}x^3