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

JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation by Substitution

  • question_answer
    If \[y=1-x+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+\frac{{{x}^{4}}}{4!}-\]....., then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] [Karnataka CET 2003]

    A)            \[x\]

    B)            \[-x\]

    C)            \[-y\]

    D)            \[y\]

    Correct Answer: D

    Solution :

               \[y=1-x+\frac{{{x}^{2}}}{(2)!}-\frac{{{x}^{2}}}{(3)!}+............\]            Þ  \[y={{e}^{-x}}\]  Þ \[\frac{dy}{dx}={{e}^{-x}}(-1)\]                    and \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=(-1)\{{{e}^{-x}}.(-1)\}\]\[={{e}^{-x}}=y\].


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