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

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

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

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

2 x y - x^{3}

Solution steps

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

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

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

= 2 x y - x^{3}

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