2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Differentiation

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

  • question_answer
    If \[y=\frac{\sqrt{{{x}^{2}}+1}+\sqrt{{{x}^{2}}-1}}{\sqrt{{{x}^{2}}+1}-\sqrt{{{x}^{2}}-1}}\], then \[\frac{dy}{dx}=\]

    A)            \[2x+\frac{2{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\]

    B)            \[2x+\frac{{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\]

    C)            \[x+\frac{2{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\]

    D)            None of these

    Correct Answer: A

    Solution :

               Rationalising, \[y=\frac{2{{x}^{2}}+2\sqrt{{{x}^{4}}-1}}{2}={{x}^{2}}+{{({{x}^{4}}-1)}^{1/2}}\]                    Þ \[\frac{dy}{dx}=2x+\frac{2{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner