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

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

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

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

e^{x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

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) = x

= x e^{x y} x

Simplify

x e^{x y} x : e^{x y} x^{2}

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

\frac{d}{d x} (- \frac{2}{3} x^{3})

\int (\frac{4}{2 x - 1}) d x

\int_{1}^{2} \frac{x ^{2} - 1}{x + 1} d x

y = x^{9 x}

\int \frac{( ln ( x ) ) ^{3}}{3 x} d x

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