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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 3 x^{2} - 2 y^{2} - 0

Simplify

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

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