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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2026 · Mathematics · Continuity and Differentiability

What is the derivative of (x)/(|x|) with respect to x , where x< 0 ?

What is the derivative of x∣x∣\dfrac{x}{|x|} with respect to xx, where x<0x< 0 ?

Options

  1. A−1-1
  2. B00
  3. C11
  4. Dxx

Correct answer

B. 00

Step-by-step solution

Given function is f(x)=x∣x∣f(x) = \dfrac{x}{|x|}.

For x<0x < 0, the absolute value function is defined as ∣x∣=−x|x| = -x.

Substituting this into the function gives f(x)=x−x=−1f(x) = \dfrac{x}{-x} = -1.

Differentiating with respect to xx gives ddx(−1)=0\dfrac{d}{dx}(-1) = 0.

Answer: 00
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