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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differentiation

NDA 2019 · Mathematics · Differentiation

What is the derivative of ^2 ( ^ -1 x) with respect to x ?

What is the derivative of sec⁡2\sec ^2\left(\tan ^{-1}x\right)withrespecttowith respect tox ?

Options

  1. A2 x
  2. Bx2+1x^2+1
  3. Cx+1\mathrm{x}+1
  4. Dx2x^2

Correct answer

A. 2 x

Step-by-step solution

Let y=sec⁡2(tan⁡−1x)\mathrm{y}=\sec ^2\left(\tan ^{-1} \mathrm{x}\right) Let tan⁡−1x=θ⇒x=tan⁡θy=sec⁡2θ=1+tan⁡2θ=1+x2∴dydx=ddx(1+x2)=2x\begin{aligned} & \text{ Let } \tan ^{-1} x=\theta \Rightarrow x=\tan \theta \\ & y=\sec ^2 \theta=1+\tan ^2 \theta=1+x^2 \\ & \therefore \frac{d y}{d x}=\frac{d}{d x}\left(1+x^2\right)=2 x\end{aligned}$$
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