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Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Fill in the blanks question  24 maths

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Answer: The correct answer is  \frac{1}{x}

Hint:  Differentiate the function but u should not be equal to zero

Given: \mathrm{y}=\log _{\mathrm{e}}|\mathrm{x}|


\mathrm{y}=\log |\mathrm{x}|=\left(\begin{array}{cc} \log (-x), & x<0 \\ \log (x), & x>0 \end{array}\right)

\frac{d y}{d x}=\left(\begin{array}{cc} \frac{-1}{-x}=\frac{1}{x},, & x<0 \\ \frac{1}{x}, & x>0 \end{array}\right)

Which means it is equal to  \frac{1}{x}  when x\neq 0

\frac{d}{d x} \log |x|=\frac{1}{x}, x \neq 0

So the answer is \frac{1}{x}


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