What is the derivative of (3x^4-2(1+4x^3)) ?

The derivative of (3x^4-2(1+4x^3)) is 12x^3+84x^6-24x^2

What is the first derivative of (3x^4-2(1+4x^3)) ?

The first derivative of (3x^4-2(1+4x^3)) is 12x^3+84x^6-24x^2

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\frac{d}{d x} ((3 x^{4} - 2) (1 + 4 x^{3}))

12 x^{3} + 84 x^{6} - 24 x^{2}

Solution steps

\frac{d}{d x} ((3 x^{4} - 2) (1 + 4 x^{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{4} - 2, g = 1 + 4 x^{3}

= \frac{d}{d x} (3 x^{4} - 2) (1 + 4 x^{3}) + \frac{d}{d x} (1 + 4 x^{3}) (3 x^{4} - 2)

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

\frac{d}{d x} (1 + 4 x^{3}) = 12 x^{2}

= 12 x^{3} (1 + 4 x^{3}) + 12 x^{2} (3 x^{4} - 2)

Simplify

12 x^{3} (1 + 4 x^{3}) + 12 x^{2} (3 x^{4} - 2) : 12 x^{3} + 84 x^{6} - 24 x^{2}

= 12 x^{3} + 84 x^{6} - 24 x^{2}

- \frac{14}{x ^{3}}

4 x^{5} + 11

\frac{\partial}{\partial x} (- 8 d (J + \frac{1}{2})^{2})

y^{^{'}} - 5 y = e^{- 2 x} y^{- 2}

\frac{d}{d x} (e^{x} + ln (x) - \frac{1}{x})

What is the derivative of (3x^4-2(1+4x^3)) ?
The derivative of (3x^4-2(1+4x^3)) is 12x^3+84x^6-24x^2
What is the first derivative of (3x^4-2(1+4x^3)) ?
The first derivative of (3x^4-2(1+4x^3)) is 12x^3+84x^6-24x^2