Question:medium

If \( y = \sin^{-1}\left(\frac{1}{\sqrt{x+1}}\right) \) then \( \frac{dy}{dx} = \)

Show Hint

For inverse trigonometric derivatives, always simplify \( 1-u^2 \) carefully before substituting.
Updated On: Apr 28, 2026
  • \( \frac{1}{2\sqrt{1-x}} \)
  • \( \frac{1}{2\sqrt{x}(1+\sqrt{x})} \)
  • \( \frac{1}{2x(1+\sqrt{x})} \)
  • \( -\frac{1}{2\sqrt{x}(1+x)} \)
Show Solution

The Correct Option is D

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