NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q1
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 1
Differentiate \(\left(3 x^{2} - 9 x + 5\right)^{9}\) with respect to x; on R.
💡 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: \(\left(54 x - 81\right) \left(3 x^{2} - 9 x + 5\right)^{8}\)
- Work on R.
- Power and chain rules: \(\frac{d}{d x} \left(3 x^{2} - 9 x + 5\right)^{9}\) = \(9 \left(3 x^{2} - 9 x + 5\right)^{8}\) × \(6 x - 9\) = \(\left(54 x - 81\right) \left(3 x^{2} - 9 x + 5\right)^{8}\).
- Combining the terms gives y′ = \(\left(54 x - 81\right) \left(3 x^{2} - 9 x + 5\right)^{8}\).
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