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

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

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

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

2 y e^{x y} + e^{x y} x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = e^{x y}

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

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

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

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

\int (5 x^{2} - 4 x) e^{2 x} d x

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\frac{d}{d x} (\frac{2 x}{e ^{x}})

\frac{x}{x ^{2} + 5}

\int cos^{12} (x) sin^{15} (x) d x

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