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

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

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

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

2 y x - 3 x^{2}

Solution steps

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

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} (x^{3})

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

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

= 2 y x - 3 x^{2}

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