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

The derivative of (3x^3+2x)(x-2)(x+4) is 15x^4+24x^3-66x^2+8x-16

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

The first derivative of (3x^3+2x)(x-2)(x+4) is 15x^4+24x^3-66x^2+8x-16

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derivative of

(3 x^{3} + 2 x) (x - 2) (x + 4)

15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x^{3} + 2 x) = 9 x^{2} + 2

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

= (9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x)

Simplify

(9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x) : 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

= 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

cos (x) d x - sin (y) d y = 0

\int arcsin (d) x d x

n \to \infty lim (1 - n)

\frac{d y}{d x} = \frac{3 - y}{2 x}

What is the derivative of (3x^3+2x)(x-2)(x+4) ?
The derivative of (3x^3+2x)(x-2)(x+4) is 15x^4+24x^3-66x^2+8x-16
What is the first derivative of (3x^3+2x)(x-2)(x+4) ?
The first derivative of (3x^3+2x)(x-2)(x+4) is 15x^4+24x^3-66x^2+8x-16