What is the derivative of 1/(arctan(2x+1)) ?

The derivative of 1/(arctan(2x+1)) is -1/(arctan^2(2x+1)(2x^2+2x+1))

What is the first derivative of 1/(arctan(2x+1)) ?

The first derivative of 1/(arctan(2x+1)) is -1/(arctan^2(2x+1)(2x^2+2x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{arctan ( 2 x + 1 )}

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

Solution steps

\frac{d}{d x} (\frac{1}{arctan ( 2 x + 1 )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{arctan ^{2} ( 2 x + 1 )} \cdot \frac{1}{2 x ^{2} + 2 x + 1} : - \frac{1}{arctan ^{2} ( 2 x + 1 ) ( 2 x ^{2} + 2 x + 1 )}

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

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