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

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

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

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

x^{2} + 2 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} + 2 x y

\int x (5 x^{2} + 4)^{3} d x

(1, 2.5), (4, 1)

\int 3 x^{3} - 12 x d x

\frac{4}{s ^{2} ( s + 2 )}

y^{^{''}} - 4 y = 16 x e^{2 x}

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