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Question

Question: \(\frac{d}{dx}{\cos h}^{- 1}(\sec x)\) =...

ddxcos⁡h−1(sec⁡x)\frac{d}{dx}{\cos h}^{- 1}(\sec x) =

A

sec⁡x\sec x

B

sin⁡x\sin x

C

tan⁡x\tan x

D

cosecxc\text{osec}x

Answer

sec⁡x\sec x

Explanation

Solution

We know that ddxcos⁡h−1x=1x2−1\frac{d}{dx}{\cos h}^{- 1}x = \frac{1}{\sqrt{x^{2} - 1}},

ddxcosh⁡−1(sec⁡x)=1sec⁡2x−1sec⁡xtan⁡x\frac{d}{dx}\cosh^{- 1}(\sec x) = \frac{1}{\sqrt{\sec^{2}x - 1}}\sec x\tan x=sec⁡xtan⁡xtan⁡x=sec⁡x\frac{\sec x\tan x}{\tan x} = \sec x.