What is (\partial)/(\partial x)(x^6-8x^3y) ?

The answer to (\partial)/(\partial x)(x^6-8x^3y) is 6x^5-24yx^2

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(\partial)/(\partial x)(x^6-8x^3y)

\frac{\partial}{\partial x} (x^{6} - 8 x^{3} y)

6 x^{5} - 24 y x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{6} - 8 x^{3} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6}) - \frac{\partial}{\partial x} (8 x^{3} y)

\frac{\partial}{\partial x} (x^{6}) = 6 x^{5}

\frac{\partial}{\partial x} (8 x^{3} y) = 24 y x^{2}

= 6 x^{5} - 24 y x^{2}

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What is (\partial)/(\partial x)(x^6-8x^3y) ?
The answer to (\partial)/(\partial x)(x^6-8x^3y) is 6x^5-24yx^2