What is derivative of arctan(sec(x+tan(x))) ?

The answer to derivative of arctan(sec(x+tan(x))) is -1/(((sec(x)+tan(x))^2+1)(-1+sin(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of arctan(sec(x+tan(x)))

\frac{d}{d x} (arctan (sec (x) + tan (x)))

- \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

Solution steps

\frac{d}{d x} (arctan (sec (x) + tan (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= \frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} (- \frac{1}{- 1 + sin ( x )})

Simplify

\frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} (- \frac{1}{- 1 + sin ( x )}) : - \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

= - \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

What is derivative of arctan(sec(x+tan(x))) ?
The answer to derivative of arctan(sec(x+tan(x))) is -1/(((sec(x)+tan(x))^2+1)(-1+sin(x)))