CUET · MATHS · PYQ PAPER 2023
If \(y=\tan ^{-1} x\) then \(\frac{d y}{d x}\) at \(y=\frac{\pi}{3}\) is equal to :
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{1}{3}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{1}{1+x^2}\) When \(y=\frac{\pi}{3}\), \(x=\tan\left(\frac{\pi}{3}\right) = \sqrt{3}\) \(\frac{dy}{dx} = \frac{1}{1+(\sqrt{3})^2} = \frac{1}{1+3} = \frac{1}{4}\)
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