Question

If \( y = \cos^{-1} x \), find \( \frac{d^2y}{dx^2} \) in terms of \( y \).

• A. \(-\csc^2 y \cot y\)
• B. \(\csc^2 y \cot y\)
• C. \(-\csc y \cot^2 y\)
• D. \(\csc y \cot^2 y\)

Hint:

For second derivatives in inverse trig functions, always convert to \(x = f(y)\) first. It makes chain rule application much cleaner and avoids messy algebra.

Answer 1

The Correct Option is A