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

  • question_answer
    If \[f(x)=3{{e}^{{{x}^{2}}}}\],then \[f'(x)-2xf(x)+\frac{1}{3}f(0)-f'(0)=\]

    A)            0

    B)            1

    C)            \[\frac{7}{3}{{e}^{{{x}^{2}}}}\]

    D)            None of these

    Correct Answer: B

    Solution :

               We have \[f(x)=3{{e}^{{{x}^{2}}}}.\]Differentiating w.r.t. x, we get \[f'(x)=6x{{e}^{{{x}^{2}}}}\]; \[\therefore f(0)=3\]and\[f'(0)=0\]                    Þ\[f'(x)-2xf(x)+\frac{1}{3}f(0)-f'(0)\]                     \[=6x{{e}^{{{x}^{2}}}}-6x{{e}^{{{x}^{2}}}}+\frac{1}{3}(3)-0=1\] .


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