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

The answer to (\partial)/(\partial x)(3x^2y-y^3) is 6xy

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

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

6 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

\frac{\partial}{\partial x} (y^{3}) = 0

= 6 y x - 0

Simplify

= 6 x y

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What is (\partial)/(\partial x)(3x^2y-y^3) ?
The answer to (\partial)/(\partial x)(3x^2y-y^3) is 6xy