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

  • question_answer
    For the curve \[\sqrt{x}+\sqrt{y}=1,\frac{dy}{dx}\]at \[\left( \frac{1}{4},\frac{1}{4} \right)\]is [Karnataka CET 1993]

    A)            ½

    B)            1

    C)            ?1

    D)            2

    Correct Answer: C

    Solution :

               \[\sqrt{x}+\sqrt{y}=1\] Þ \[\frac{dy}{dx}=-\frac{\sqrt{y}}{\sqrt{x}}\] Þ  \[{{\left( \frac{dy}{dx} \right)}_{\left( \frac{1}{4},\,\frac{1}{4} \right)}}=-1\].


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