What is (\partial)/(\partial x)(4y-4x^3) ?

The answer to (\partial)/(\partial x)(4y-4x^3) is -12x^2

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(\partial)/(\partial x)(4y-4x^3)

\frac{\partial}{\partial x} (4 y - 4 x^{3})

- 12 x^{2}

Solution steps

\frac{\partial}{\partial x} (4 y - 4 x^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 y) - \frac{\partial}{\partial x} (4 x^{3})

\frac{\partial}{\partial x} (4 y) = 0

\frac{\partial}{\partial x} (4 x^{3}) = 12 x^{2}

= 0 - 12 x^{2}

Simplify

= - 12 x^{2}

What is (\partial)/(\partial x)(4y-4x^3) ?
The answer to (\partial)/(\partial x)(4y-4x^3) is -12x^2