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

  • question_answer
    \[\frac{d}{dx}\left[ \log \sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\]                             [BIT Ranchi 1990]

    A)            \[\sec x\]

    B)            \[\cos \text{ec}\,x\]

    C)            \[\cos \text{ec}\frac{x}{2}\]

    D)            \[\sec \frac{x}{2}\]

    Correct Answer: B

    Solution :

               \[\frac{d}{dx}\left[ \log \sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\frac{d}{dx}\left[ \log \left( \tan \frac{x}{2} \right) \right]=\text{cosec}\,x\].


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