AP EAMCET · Maths · Differentiation
The derivative of \(\tan ^{-1}\left[\frac{x}{1+\sqrt{1-x^2}}\right]\) with respect to \(\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)\) is
- A \(\frac{1}{2}\)
- B \(\frac{1}{4}\)
- C \(\frac{-1}{4}\)
- D \(\frac{-1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{-1}{4}\)
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} y & =\tan ^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right) \\ u & =\sec ^{-1}\left(\frac{1}{2 x^2-1}\right) \end{aligned}\) Let \(x=\cos \theta\)…
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