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

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

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

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

y^{3} - 2 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y^{3} - 2 y x

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