NCERT Class 12 · Ch 5 Exercise 5.4 · Q8
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.4 Question 8
Differentiate \(\log{\left(\log{\left(x \right)} \right)}\) with respect to x; for x>1.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(\frac{1}{x \log{\left(x \right)}}\)
- Work for x>1.
- Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \log{\left(\log{\left(x \right)} \right)}\) = \(\frac{1}{x \log{\left(x \right)}}\).
- Combining the terms gives y′ = \(\frac{1}{x \log{\left(x \right)}}\).
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