AP EAMCET · Maths · Differentiation
The derivative of \(\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)\) with respect to \(\sqrt{1-x^2}\) at \(x=\frac{1}{2}\) equals
- A \(2\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
Let \(u=\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)\) and \(v=\sqrt{1-x^2}\) Put \(x=\cos \theta\) \(\therefore \quad u=\sec ^{-1}\left(\frac{1}{2 \cos ^2 \theta-1}\right)\) and \(v=\sqrt{1-\cos ^2 \theta}\)…
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