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

  • question_answer
    \[\frac{d}{dx}\left( {{\cos }^{-1}}\sqrt{\frac{1+\cos x}{2}} \right)=\]                                [AI CBSE 1982]

    A)            1

    B)            \[\frac{1}{2}\]

    C)            \[\frac{1}{3}\]

    D)            None of these

    Correct Answer: B

    Solution :

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


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