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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Differentiation

JEE Advanced · Mathematics · Differentiation

If y= ( ^ -1 x) , then (d y)/(d x) at x=1 is equal to:

If y=sec⁡(tan⁡−1x)y=\sec \left(\tan ^{-1} x\right), then \frac{d y}{d x} at x=1isequalto:x=1 is equal to:

Options

  1. A1
  2. B2\sqrt{2}
  3. C12\frac{1}{\sqrt{2}}
  4. D12\frac{1}{2}

Correct answer

C. 12\frac{1}{\sqrt{2}}

Step-by-step solution

By Chain rule y=sec⁡(tan⁡−1x)dydx=sec⁡(tan⁡−1x)⋅tan⁡(tan⁡−1x)⋅11+x2dydx∣x=1=2⋅1⋅12=12\begin{aligned} & y=\sec \left(\tan ^{-1} x\right) \\ & \frac{d y}{d x}=\sec \left(\tan ^{-1} x\right) \cdot \tan \left(\tan ^{-1} x\right) \cdot \frac{1}{1+x^2} \\ & \left.\frac{d y}{d x}\right|_{x=1}=\sqrt{2} \cdot 1 \cdot \frac{1}{2}=\frac{1}{\sqrt{2}}\end{aligned}
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