What is the derivative of (5x+2)(x^3+4x) ?

The derivative of (5x+2)(x^3+4x) is 20x^3+6x^2+40x+8

What is the first derivative of (5x+2)(x^3+4x) ?

The first derivative of (5x+2)(x^3+4x) is 20x^3+6x^2+40x+8

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derivative of

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

20 x^{3} + 6 x^{2} + 40 x + 8

Solution steps

\frac{d}{d x} ((5 x + 2) (x^{3} + 4 x))

Apply the Product Rule:

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

f = 5 x + 2, g = x^{3} + 4 x

= \frac{d}{d x} (5 x + 2) (x^{3} + 4 x) + \frac{d}{d x} (x^{3} + 4 x) (5 x + 2)

\frac{d}{d x} (5 x + 2) = 5

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

= 5 (x^{3} + 4 x) + (3 x^{2} + 4) (5 x + 2)

Simplify

5 (x^{3} + 4 x) + (3 x^{2} + 4) (5 x + 2) : 20 x^{3} + 6 x^{2} + 40 x + 8

= 20 x^{3} + 6 x^{2} + 40 x + 8

What is the derivative of (5x+2)(x^3+4x) ?
The derivative of (5x+2)(x^3+4x) is 20x^3+6x^2+40x+8
What is the first derivative of (5x+2)(x^3+4x) ?
The first derivative of (5x+2)(x^3+4x) is 20x^3+6x^2+40x+8