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

The derivative of (2x+3(3x-2)) is 12x+5

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

The first derivative of (2x+3(3x-2)) is 12x+5

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

12 x + 5

Solution steps

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

Apply the Product Rule:

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

f = 2 x + 3, g = 3 x - 2

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

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

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

= 2 (3 x - 2) + 3 (2 x + 3)

Simplify

2 (3 x - 2) + 3 (2 x + 3) : 12 x + 5

= 12 x + 5

What is the derivative of (2x+3(3x-2)) ?
The derivative of (2x+3(3x-2)) is 12x+5
What is the first derivative of (2x+3(3x-2)) ?
The first derivative of (2x+3(3x-2)) is 12x+5