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

The derivative of (x^3+3x(2x+4)) is 8x^3+12x^2+12x+12

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

The first derivative of (x^3+3x(2x+4)) is 8x^3+12x^2+12x+12

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

8 x^{3} + 12 x^{2} + 12 x + 12

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(3 x^{2} + 3) (2 x + 4) + 2 (x^{3} + 3 x) : 8 x^{3} + 12 x^{2} + 12 x + 12

= 8 x^{3} + 12 x^{2} + 12 x + 12

What is the derivative of (x^3+3x(2x+4)) ?
The derivative of (x^3+3x(2x+4)) is 8x^3+12x^2+12x+12
What is the first derivative of (x^3+3x(2x+4)) ?
The first derivative of (x^3+3x(2x+4)) is 8x^3+12x^2+12x+12