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

  • question_answer
    If \[f(x)=(x-{{x}_{0}})g(x)\], where \[g(x)\] is continuous at \[{{x}_{0}}\], then \[f'({{x}_{0}})\] is equal to           

    A)            0

    B)            \[{{x}_{0}}\]

    C)            \[g({{x}_{0}})\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[f'({{x}_{0}})=\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,\frac{(x-{{x}_{0}})g(x)-0}{x-{{x}_{0}}}=\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,g(x)=g({{x}_{0}})\]            Since g is continuous.


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