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NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q4

NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 4

Differentiate \(\operatorname{asin}{\left(x^{\frac{3}{2}} \right)}\) with respect to x; for 0<x<1; at 0 the right derivative is 0, while at 1 no finite left derivative exists.

💡 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: \(\frac{3 \sqrt{x}}{2 \sqrt{1 - x^{3}}}\)
  1. Work for 0<x<1; at 0 the right derivative is 0, while at 1 no finite left derivative exists.
  2. Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \operatorname{asin}{\left(x^{\frac{3}{2}} \right)}\) = \(\frac{3 \sqrt{x}}{2 \sqrt{1 - x^{3}}}\).
  3. Combining the terms gives y′ = \(\frac{3 \sqrt{x}}{2 \sqrt{1 - x^{3}}}\).

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