What is the derivative of (3x^2+3x-1*(2x+3)) ?

The derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7

What is the first derivative of (3x^2+3x-1*(2x+3)) ?

The first derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((3 x^{2} + 3 x - 1) \cdot (2 x + 3))

18 x^{2} + 30 x + 7

Solution steps

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

Apply the Product Rule:

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

f = 3 x^{2} + 3 x - 1, g = 2 x + 3

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

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

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

= (6 x + 3) (2 x + 3) + 2 (3 x^{2} + 3 x - 1)

Simplify

(6 x + 3) (2 x + 3) + 2 (3 x^{2} + 3 x - 1) : 18 x^{2} + 30 x + 7

= 18 x^{2} + 30 x + 7

What is the derivative of (3x^2+3x-1*(2x+3)) ?
The derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7
What is the first derivative of (3x^2+3x-1*(2x+3)) ?
The first derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7