Question:medium
If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)
If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)
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Whenever you see \(\sqrt{x^2 - 1}\) in an inverse trig function, substituting \(x = \sec \theta\) is almost always the fastest path to simplification.
Updated On: Jun 24, 2026
- \(\frac{1}{x^2}\)
- \(\frac{1}{x^4}\)
- \(\frac{-1}{x^2}\)
- \(\frac{-1}{x^4}\)
- \(\frac{1}{x^3}\)
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The Correct Option is C
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