Differentiability & Derivatives of Composite Functions

Grade 12 Maths Higher — Differentiability & Derivatives of Composite Functions: 25 practice questions with instant scoring and explanations.

1. The derivative f'(a) is defined as:
2. If f is differentiable at a, then f is:
3. f(x) = |x| is differentiable at x = 0:
4. The function f(x) = x^(1/3) at x = 0:
5. If f and g are differentiable at a, then (f+g) is:
6. The product rule states (fg)' =
7. The quotient rule states (f/g)' =
8. The chain rule states (f∘g)'(x) =
9. If y = sin(x²), then dy/dx =
10. The derivative of e^(3x) is:
11. d/dx[ln(x)] =
12. The derivative of tan(x) is:
13. If f(x) = sin⁻¹(x), then f'(x) =
14. The second derivative f''(x) is:
15. For y = x^n, dy/dx =
16. The derivative of a constant c is:
17. If f(x) = e^x, then f'(x) =
18. The derivative of cot(x) is:
19. Right derivative f'₊(a) is:
20. For f to be differentiable at a, the one-sided derivatives must:
21. Rolle's Theorem requires:
22. If f satisfies Rolle's Theorem conditions, then there exists c ∈ (a,b) with:
23. Mean Value Theorem conclusion is:
24. The derivative of log_a(x) is:
25. Review question for Differentiability & Derivatives of Composite Functions