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

  • question_answer
    The derivative of \[f(x)=|x{{|}^{3}}\] at \[x=0\] is [RPET 2001; Kurukshetra CEE 2002]

    A)            0

    B)            1

    C)            ?1

    D)            Not defined

    Correct Answer: A

    Solution :

               \[f(x)\,=\,|x{{|}^{3}}\] Þ \[{f}'(x)=3|x{{|}^{2}}\frac{d}{dx}|x|\]            At \[x=0\], \[{f}'(x)=0.\frac{d}{dx}|x|\], \[{f}'(x)=0\].


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