MHT CET · Maths · Differentiation
The derivative of \(\log |x|\) is
- A \(\frac{1}{x}, x>0\)
- B \(\frac{1}{|x|}, x \neq 0\)
- C \(\frac{1}{x}, x \neq 0\)
- D None of these
Answer & Solution
Correct Answer
(C) \(\frac{1}{x}, x \neq 0\)
Step-by-step Solution
Detailed explanation
We have, \(y=\log |x|=\left\{\begin{array}{ll}\log x & , x>0 \\ \log (-x), & x < 0\end{array}\right.\)
\(\therefore \quad \frac{d y}{d x}=\frac{1}{x}, x>0 \)
\( \frac{1}{-x}(-1)=\frac{1}{x}, x < 0 \)
\( \Rightarrow \quad \frac{d y}{d x}=\frac{1}{x}, x \neq 0\)
\(\therefore \quad \frac{d y}{d x}=\frac{1}{x}, x>0 \)
\( \frac{1}{-x}(-1)=\frac{1}{x}, x < 0 \)
\( \Rightarrow \quad \frac{d y}{d x}=\frac{1}{x}, x \neq 0\)
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