AP EAMCET · Maths · Differentiation
If \(\mathrm{y}=\log \left(\sec \left(\operatorname{Tan}^{-1} \mathrm{x}\right)\right)(\mathrm{x}>0)\), then \(\frac{\mathrm{dy}}{\mathrm{dx}}\) at \(\mathrm{x}=1\) is
- A \(1\)
- B \(3\)
- C \(\frac{1}{2}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{d}{dx} \left( \log \left( \sec \left( \operatorname{Tan}^{-1} x \right) \right) \right)\) \(= \frac{1}{\sec(\operatorname{Tan}^{-1} x)} \cdot \sec(\operatorname{Tan}^{-1} x) \tan(\operatorname{Tan}^{-1} x) \cdot \frac{1}{1+x^2}\)…
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