What is (\partial)/(\partial y)(3x^2y+2xy^2) ?

The answer to (\partial)/(\partial y)(3x^2y+2xy^2) is 3x^2+4xy

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(\partial)/(\partial y)(3x^2y+2xy^2)

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

3 x^{2} + 4 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (2 x y^{2}) = 4 x y

= 3 x^{2} + 4 x y

\int (2 x + 1)^{2} d x

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What is (\partial)/(\partial y)(3x^2y+2xy^2) ?
The answer to (\partial)/(\partial y)(3x^2y+2xy^2) is 3x^2+4xy