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NCERT Class 12 · Ch 5 Exercise 5.2 · Q8

NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.2 Question 8

Differentiate \(\cos{\left(\sqrt{x} \right)}\) with respect to x; for x>0 (the right derivative at x=0 is −1/2).

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: \(- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\)
  1. Work for x>0 (the right derivative at x=0 is −1/2).
  2. Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \cos{\left(\sqrt{x} \right)}\) = \(- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\).
  3. Combining the terms gives y′ = \(- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\).

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