CUET · MATHS · PYQ PAPER 2025
The value of derivative of the function \(\cot ^{-1}\left\{(\cos 2 x)^{1 / 2}\right\}\) at \(x=\frac{\pi}{6}\) is
- A \(\left(\frac{2}{3}\right)^{\frac{1}{2}}\)
- B \(\left(\frac{1}{3}\right)^{\frac{1}{2}}\)
- C \(3^{\frac{1}{2}}\)
- D \(6^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{2}{3}\right)^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\(y = \cot^{-1}\left\{ (\cos 2 x)^{1 / 2}\right\}\) \(\frac{dy}{dx} = -\frac{1}{1+(\cos 2x)^{1/2})^2} \cdot \frac{d}{dx} (\cos 2x)^{1/2}\) \(\frac{dy}{dx} = -\frac{1}{1+\cos 2x} \cdot \frac{1}{2}(\cos 2x)^{-1/2} \cdot (-\sin 2x) \cdot 2\)…
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