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

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

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

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

3 x y^{2} - x^{2}

Solution steps

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

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

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

= 3 x y^{2} - x^{2}

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