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NDA2026MathematicsContinuity and DifferentiabilityActual

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

Options

  1. A-1
  2. B0
  3. C1
  4. Dx

Correct answer

B. 0

Step-by-step solution

Given function is f(x) = x |x| . For x Substituting this into the function gives f(x) = x -x = -1 . Differentiating with respect to x gives d dx (-1) = 0 . Answer: 0

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