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

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

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

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

2 y x - y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x - y^{2}

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