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

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

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

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

12 x^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 12 x^{2} - 0

Simplify

= 12 x^{2}

\frac{\partial}{\partial x} (e^{y} - y e^{x})

(a - 1) + 1

y^{^{'}} + \frac{2 y}{t + 2} = (t + 2)^{5}, y (0) = 5

\frac{1}{s ^{3} + 4 s}

\int 7 x^{5} e^{x} d x

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