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

  • question_answer
    If \[f(1)=3,\,{f}'(1)=2,\]then \[\frac{d}{dx}\{\log f\,({{e}^{x}}+2x)\}\] at \[x=0\] is                                                               [AMU 1999]

    A)            2 / 3

    B)            3 / 2

    C)          2

    D)            0

    Correct Answer: C

    Solution :

               Let \[y=\frac{d}{dx}\{\log f({{e}^{x}}+2x)\}=\frac{{f}'({{e}^{x}}+2x)({{e}^{x}}+2)}{f({{e}^{x}}+2x)}\]            \[\therefore \,\,{{(y)}_{x=0}}\] = \[\frac{1}{f(1)}.{f}'(1).3\] = \[\frac{2}{3}.3=2\].


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