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

  • question_answer
    If \[f(x)={{e}^{x}}g(x),g(0)=2,g'(0)=1\], then \[f'(0)\]is

    A)            1

    B)            3

    C)            2

    D)            0

    Correct Answer: B

    Solution :

               \[f(x)={{e}^{x}}g(x)\Rightarrow f'(x)={{e}^{x}}g(x)+{{e}^{x}}g'(x)\]                    \[\Rightarrow f'(0)=g(0)+g'(0)=2+1=3\].


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