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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differentiation

NDA 2023 · Mathematics · Differentiation

If f(x)=| | x| | where 0 < x < 1 , then what is f^ (0.5) equal to?

If f(x)=∣ln⁡∣x∣∣f(x)=|\ln | x| | where 0<x<10 < \mathrm{x} < 1, then what is f′(0.5)f^{\prime}(0.5) equal to?

Options

  1. A-2
  2. B-1
  3. C0
  4. D2

Correct answer

A. -2

Step-by-step solution

f(x)=∣ln⁡∣x∣∣;0<x<1⇒f(x)=−ln⁡x\mathrm{f}(\mathrm{x})=|\ln | \mathrm{x}| | ; 0 < \mathrm{x} < 1 \Rightarrow \mathrm{f}(\mathrm{x})=-\ln \mathrm{x} Now, \mathrmf′(x)=−1x⇒\mathrmf′(0.5)=−2\mathrmf^{\prime}(\mathrm{x})=\frac{-1}{x} \Rightarrow \mathrmf^{\prime}(0.5)=-2
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