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

The derivative of (3x^4-4(3-2x^3)) is 36x^3-42x^6+24x^2

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

The first derivative of (3x^4-4(3-2x^3)) is 36x^3-42x^6+24x^2

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

36 x^{3} - 42 x^{6} + 24 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (3 - 2 x^{3}) = - 6 x^{2}

= 12 x^{3} (3 - 2 x^{3}) + (- 6 x^{2}) (3 x^{4} - 4)

Simplify

12 x^{3} (3 - 2 x^{3}) + (- 6 x^{2}) (3 x^{4} - 4) : 36 x^{3} - 42 x^{6} + 24 x^{2}

= 36 x^{3} - 42 x^{6} + 24 x^{2}

y = x cos (x) sin (x)

\frac{\partial}{\partial y} (4 y (\frac{1}{x} - ln (x)))

\int_{0}^{9} \frac{1}{x} d x

y = sec (x) tan (x)

\int 7 e^{3 x} d x

What is the derivative of (3x^4-4(3-2x^3)) ?
The derivative of (3x^4-4(3-2x^3)) is 36x^3-42x^6+24x^2
What is the first derivative of (3x^4-4(3-2x^3)) ?
The first derivative of (3x^4-4(3-2x^3)) is 36x^3-42x^6+24x^2