AP EAMCET · Maths · Differentiation
The derivative of \(y=\sin ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{2}\right)\) is
- A \(\frac{1}{\sqrt{1+x^2}}\)
- B \(\frac{1}{\sqrt{1-x^2}}\)
- C \(\frac{1}{2 \sqrt{1+x^2}}\)
- D \(\frac{1}{2 \sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2 \sqrt{1-x^2}}\)
Step-by-step Solution
Detailed explanation
\(y=\sin ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{2}\right)\) Put, \(x=\cos 2 \theta \Rightarrow 2 \theta=\cos ^{-1} x\)…
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