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

The derivative of (3x^2+3x-2(2x-1)(-2x)) is -48x^3-18x^2+28x-4

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

The first derivative of (3x^2+3x-2(2x-1)(-2x)) is -48x^3-18x^2+28x-4

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

- 48 x^{3} - 18 x^{2} + 28 x - 4

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((2 x - 1) (- 2 x)) = - 8 x + 2

= (6 x + 3) (2 x - 1) (- 2 x) + (- 8 x + 2) (3 x^{2} + 3 x - 2)

Simplify

(6 x + 3) (2 x - 1) (- 2 x) + (- 8 x + 2) (3 x^{2} + 3 x - 2) : - 48 x^{3} - 18 x^{2} + 28 x - 4

= - 48 x^{3} - 18 x^{2} + 28 x - 4

What is the derivative of (3x^2+3x-2(2x-1)(-2x)) ?
The derivative of (3x^2+3x-2(2x-1)(-2x)) is -48x^3-18x^2+28x-4
What is the first derivative of (3x^2+3x-2(2x-1)(-2x)) ?
The first derivative of (3x^2+3x-2(2x-1)(-2x)) is -48x^3-18x^2+28x-4