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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    If \[f(x)={{\tan }^{-1}}\left( \frac{\sin x}{1+\cos x} \right)\],then \[f'\left( \frac{\pi }{3} \right)=\]          [BIT Ranchi 1990]

    A)            \[\frac{1}{2(1+\cos x)}\]

    B)            \[\frac{1}{2}\]

    C)            \[\frac{1}{4}\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[f(x)={{\tan }^{-1}}\left( \frac{\sin x}{1+\cos x} \right)={{\tan }^{-1}}\left[ \tan \frac{x}{2} \right]=\frac{x}{2}\]                    Þ \[f'(x)=\frac{1}{2}.\] Hence \[f'\left( \frac{\pi }{3} \right)=\frac{1}{2}\].


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