NDA 2024 · PYQ · Composition of Functions / Differentiation · medium
Let f(x) and g(x) be two functions such that g(x) = x - 1/x and f∘g(x) = x³ - 1/x³. What is f''(x) equal to?
- A.-2/x³
- B.2x + 2/x³
- C.6x + 3
- D.6x✓ Correct
From f(g(x)) = x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x), we identify f(t) = t³ + 3t. So f(x) = x³ + 3x. Then f'(x) = 3x² + 3 and f''(x) = 6x.
💡
Practice unlimited NDA PYQs + AI-tracked progress on each topic.
Sign up free →Want more NDA practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English