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

  • question_answer
    If \[y=(1+{{x}^{1/4}})(1+{{x}^{1/2}})(1-{{x}^{1/4}})\], then \[\frac{dy}{dx}\]= [MP PET 1994]

    A)            1

    B)            ? 1

    C)            x

    D)            \[\sqrt{x}\]

    Correct Answer: B

    Solution :

               \[y=(1+{{x}^{1/4}})(1+{{x}^{1/2}})(1-{{x}^{1/4}})\]                    Þ \[y=(1+{{x}^{1/4}})(1-{{x}^{1/4}})(1+{{x}^{1/2}})\]                         \[=(1-{{x}^{1/2}})(1+{{x}^{1/2}})=1-x\Rightarrow \frac{dy}{dx}=-1\].


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