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}

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