Solveeit Logo
Login

Question

Question: \[\frac{d}{dx}\tan^{- 1}\left\lbrack \frac{\cos x - \sin x}{\cos x + \sin x} \right\rbrack\]...

ddxtan⁡−1[cos⁡x−sin⁡xcos⁡x+sin⁡x]\frac{d}{dx}\tan^{- 1}\left\lbrack \frac{\cos x - \sin x}{\cos x + \sin x} \right\rbrack

A

12(1+x2)\frac{1}{2(1 + x^{2})}

B

11+x2\frac{1}{1 + x^{2}}

C

1

D

– 1

Answer

– 1

Explanation

Solution

ddxtan⁡−1[cos⁡x−sin⁡xcos⁡x+sin⁡x]=ddxtan⁡−1[tan⁡(π4−x)]=−1\frac{d}{dx}\tan^{- 1}\left\lbrack \frac{\cos x - \sin x}{\cos x + \sin x} \right\rbrack = \frac{d}{dx}\tan^{- 1}\left\lbrack \tan\left( \frac{\pi}{4} - x \right) \right\rbrack = - 1..