What is the derivative of (3x+1(2x+6)) ?

The derivative of (3x+1(2x+6)) is 12x+20

What is the first derivative of (3x+1(2x+6)) ?

The first derivative of (3x+1(2x+6)) is 12x+20

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\frac{d}{d x} ((3 x + 1) (2 x + 6))

12 x + 20

Solution steps

\frac{d}{d x} ((3 x + 1) (2 x + 6))

Apply the Product Rule:

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

f = 3 x + 1, g = 2 x + 6

= \frac{d}{d x} (3 x + 1) (2 x + 6) + \frac{d}{d x} (2 x + 6) (3 x + 1)

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

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

= 3 (2 x + 6) + 2 (3 x + 1)

Simplify

3 (2 x + 6) + 2 (3 x + 1) : 12 x + 20

= 12 x + 20

What is the derivative of (3x+1(2x+6)) ?
The derivative of (3x+1(2x+6)) is 12x+20
What is the first derivative of (3x+1(2x+6)) ?
The first derivative of (3x+1(2x+6)) is 12x+20