What is (\partial)/(\partial y)(xy^2+x^2y) ?

The answer to (\partial)/(\partial y)(xy^2+x^2y) is 2xy+x^2

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(\partial)/(\partial y)(xy^2+x^2y)

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

2 x y + x^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 2 x y + x^{2}

\frac{\partial}{\partial x} (x^{2} y - x^{3})

\frac{\partial}{\partial x} (6 x y^{2} - 2 x^{3} - 3 y^{4})

\frac{d ^{2} y}{d x ^{2}} = 3

\frac{\partial}{\partial x} (2 x + 4 y)

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

What is (\partial)/(\partial y)(xy^2+x^2y) ?
The answer to (\partial)/(\partial y)(xy^2+x^2y) is 2xy+x^2