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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differentiation

NDA 2023 · Mathematics · Differentiation

Paragraph: Let f(x)=| x|, x ≠ 1 Question: What is the derivative of...

Paragraph: Let f(x)=∣ln⁡x∣,x≠1f(x)=|\ln x|, x \neq 1
Question: What is the derivative of f(x)f(x) at x=0.5x=0.5 ?

Options

  1. A−2-2
  2. B−1-1
  3. C11
  4. D22

Correct answer

A. −2-2

Step-by-step solution

f(x)=|\ln x|f^{\prime}(x)=\left\{ln⁡x,x>1−ln⁡x,x<1\begin{array}{rr}\ln x, & x > 1 \\ -\ln x, & x < 1\end{array}\right. for x=0.5,f(x)=−ln⁡xf′(x)=−1xf′(0.5)=−10.5=−2x=0.5, f(x)=-\ln xf^{\prime}(x)=-\frac{1}{x}f^{\prime}(0.5)=-\frac{1}{0.5}=-2
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