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

The derivative of arctan(3x+2) is 3/(9x^2+12x+5)

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

The first derivative of arctan(3x+2) is 3/(9x^2+12x+5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{3}{9 x ^{2} + 12 x + 5}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( 3 x + 2 ) ^{2} + 1} \cdot 3 : \frac{3}{9 x ^{2} + 12 x + 5}

= \frac{3}{9 x ^{2} + 12 x + 5}

What is the derivative of arctan(3x+2) ?
The derivative of arctan(3x+2) is 3/(9x^2+12x+5)
What is the first derivative of arctan(3x+2) ?
The first derivative of arctan(3x+2) is 3/(9x^2+12x+5)