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

  • question_answer
    \[\frac{d}{dx}\log |x|\text{ }=......,(x\ne 0)\]                     

    A)            \[\frac{1}{x}\]

    B)            \[-\frac{1}{x}\]

    C)            x

    D)            \[-x\]

    Correct Answer: A

    Solution :

               \[\log |x|\,=\log x\], if \[x>0\]\[=\log (-x)\], if \[x<0\]            Hence \[\frac{d}{dx}\left\{ \log |x| \right\}=\frac{1}{x}\],if \[x>0\]                                     \[=\left( \frac{1}{-x} \right)(-1)=\frac{1}{x}\],if \[x<0\]            Thus \[\frac{d}{dx}\left\{ \log |x| \right\}=\frac{1}{x}\], if \[x\ne 0\].


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