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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=2x=2 ?

Options

  1. A−12-\frac{1}{2}
  2. B−1-1
  3. C12\frac{1}{2}
  4. D22

Correct answer

C. 12\frac{1}{2}

Step-by-step solution

At x=2,f(x)=ln⁡xf′(x)=1x⇒f′(2)=12x=2, f(x)=\ln xf^{\prime}(x)=\frac{1}{x} \Rightarrow f^{\prime}(2)=\frac{1}{2}
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