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

  • question_answer
    If \[y={{\tan }^{-1}}\left( \frac{\sqrt{a}-\sqrt{x}}{1+\sqrt{ax}} \right)\], then \[\frac{dy}{dx}=\]          [AI CBSE 1988]

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

    B)            \[\frac{1}{(1+x)\sqrt{x}}\]

    C)            \[-\frac{1}{2(1+x)\sqrt{x}}\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[y={{\tan }^{-1}}\sqrt{a}-{{\tan }^{-1}}\sqrt{x}\]                    Differentiating w.r.t. x, we get, \[\frac{dy}{dx}=-\frac{1}{(1+x)}.\frac{1}{2\sqrt{x}}\].


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