Logarithmic Differentiation, Higher Order Derivatives

Grade 12 Maths Higher — Logarithmic Differentiation, Higher Order Derivatives: 25 practice questions with instant scoring and explanations.

1. Logarithmic differentiation is applied by taking ln of:
2. For y = x^(1/x), using logarithmic differentiation: dy/dx =
3. For y = (√x)/(x+1)^(1/3), logarithmic differentiation gives:
4. The second derivative f''(x) represents:
5. For f(x) = x³, f'(x) = 3x², and f''(x) =
6. The third derivative f'''(x) is denoted as:
7. For y = sin(x), the fourth derivative y^(4) =
8. The n-th derivative of e^(kx) is:
9. For polynomial of degree n, the (n+1)-th derivative is:
10. Leibniz rule for product (uv)^(n) applies:
11. For f(x) = e^(2x)·sin(x), finding f''(x) requires:
12. If f''(x) > 0 on interval I, then f is:
13. An inflection point occurs where:
14. For y = ln(x), the second derivative y'' =
15. The higher-order derivative test for extrema uses:
16. If f'(c) = 0 and f''(c) > 0, then c is:
17. Taylor series expansion uses:
18. The Taylor polynomial of degree n centered at a is:
19. For a function y = f(x), the notation d^n y/dx^n means:
20. If all derivatives of f exist and f^(n)(a) = 0 for n = 1,2,...,k but f^(k+1)(a) ≠ 0:
21. The n-th derivative of x^n is:
22. For y = (1-x)^(-1), the n-th derivative is:
23. Higher-order partial derivatives satisfy Schwarz's theorem if:
24. The Hessian matrix H of f(x,y) contains:
25. Review question for Logarithmic Differentiation, Higher Order Derivatives