If f(x)=|\ln|x|| where 0 \lt x \lt 1, then what is f'(0.5) equal to?
- A. -2 ✓
- B. -1
- C. 0
- D. 2
Correct Answer: A. -2
Explanation
For 0 \lt x \lt 1, |x| = x and \ln x is negative. Therefore, |\ln x| = -\ln x. So the function simplifies to f(x) = -\ln x. Differentiating with respect to x gives f'(x) = -\frac{1}{x}. At x=0.5, f'(0.5) = -\frac{1}{0.5} = -2.
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