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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1
If f(x)=tan⁡−1(sin⁡x1+cos⁡x)f(x)=\tan ^{-1}\left(\frac{\sin x}{1+\cos x}\right), then f′(π3)f^{\prime}\left(\frac{\pi}{3}\right) is equal to
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Correct option: B
12\frac{1}{2}
Option B is correct because the function simplifies to x/2, and its derivative is 1/2, which is constant.

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