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

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

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

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

e^{x y} x^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Simplify

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

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

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\int \frac{sin ( 2 x )}{18 + cos ^{2} ( x )} d x

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