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

The derivative of arctan(2x+3) is 1/(2x^2+6x+5)

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

The first derivative of arctan(2x+3) is 1/(2x^2+6x+5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{1}{2 x ^{2} + 6 x + 5}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( 2 x + 3 ) ^{2} + 1} \cdot 2 : \frac{1}{2 x ^{2} + 6 x + 5}

= \frac{1}{2 x ^{2} + 6 x + 5}

\int (- 9 cos (x)) d x

\int x^{2} - 9 x + 14 d x

\int \frac{x + 2}{x ^{2} + 5 x} d x

\frac{d y}{d x} = 5 x - y

\int_{0}^{6} 2 e^{x} d x

What is the derivative of arctan(2x+3) ?
The derivative of arctan(2x+3) is 1/(2x^2+6x+5)
What is the first derivative of arctan(2x+3) ?
The first derivative of arctan(2x+3) is 1/(2x^2+6x+5)