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

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

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

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

12 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 12 x^{2} - 0

Simplify

= 12 x^{2}

\frac{d y}{d x} + \frac{3 y}{x} = 6 x^{2}

sin (2 t)

\frac{\partial}{\partial x} (x^{0.75})

y^{^{''}} + 2 y^{^{'}} - y = 0, y (0) = 0, y^{^{'}} (0) = 22

x \to \frac{1}{2} lim (3 x - 5)

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