What is (\partial)/(\partial x)(4x^3+z^2) ?

The answer to (\partial)/(\partial x)(4x^3+z^2) is 12x^2

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(\partial)/(\partial x)(4x^3+z^2)

\frac{\partial}{\partial x} (4 x^{3} + z^{2})

12 x^{2}

Solution steps

\frac{\partial}{\partial x} (4 x^{3} + z^{2})

Treat

z

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} (z^{2})

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

\frac{\partial}{\partial x} (z^{2}) = 0

= 12 x^{2} + 0

Simplify

= 12 x^{2}

\frac{d}{d x} ((r (x) (x)^{2} - x^{2})^{\frac{1}{2}})

f (x) = sin (3 x), (\frac{π}{18}, \frac{2}{2})

\frac{d}{d x} (sin^{2} (b x) + x^{2} + 1)

\int \frac{3 x - 6}{x ^{2} - 4 x + 5} d x

\frac{\partial}{\partial x} (x z x + y)

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