JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y = {\rm{sec}}\left( {{{\tan }^{ - 1}}x} \right)\) then \(\frac{{dy}}{{dx}}\) at \(x = 1\) is equal to :
- A \(\frac{1}{{\sqrt 2 }}\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(\sqrt 2 \)
Answer & Solution
Correct Answer
(A) \(\frac{1}{{\sqrt 2 }}\)
Step-by-step Solution
Detailed explanation
\(y=\sec \left(\tan ^{-1} x\right)\) Let \(\quad \tan ^{-1} x=\theta\) \({x=\tan \theta} \) \({y=\sec \theta}\) \({y=\sqrt{1+x^{2}}} \) \({\frac{d y}{d x}=\frac{1}{2 \sqrt{1+x^{2}}} \cdot 2 x} \) at \({x=1}\) \(\frac{d y}{d x}=\frac{1}{\sqrt{2}}\)
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