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

  • question_answer
    If \[y={{x}^{2}}\log x+\frac{2}{\sqrt{x}},\] then \[\frac{dy}{dx}=\]

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

    B)            \[x+2x\log x-\frac{1}{{{x}^{3/2}}}\]

    C)            \[x+2x\log x-\frac{2}{{{x}^{3/2}}}\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[y={{x}^{2}}\log x+\frac{2}{\sqrt{x}}\]                    \[\frac{dy}{dx}=2x\log x+x-{{x}^{-3/2}}=x+2x\log x-\frac{1}{{{x}^{3/2}}}\].


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