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

  • question_answer
    \[\frac{d}{dx}\left[ {{\tan }^{-1}}\sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\] [BIT Ranchi 1989; Roorkee 1989; RPET 1996]

    A)            \[-\frac{1}{2}\]

    B)            0

    C)            \[\frac{1}{2}\]

    D)            1

    Correct Answer: C

    Solution :

               \[\frac{d}{dx}\left[ {{\tan }^{-1}}\sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\frac{d}{dx}\left[ {{\tan }^{-1}}\tan \frac{x}{2} \right]=\frac{1}{2}\].


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