| Questions | Answers |
|---|---|
| 1. \(f(x) = (x + 2)(3x – 1)\) | \(f'(x) = 6x + 5\) |
| 2. \(f(x) = (2x^2 + 3x)(4x – 5)\) | \(f'(x) = 24x^2 + 4x – 15\) |
| 3. \(f(x) = (x^3 – 2x)(x^2 + 5)\) | \(f'(x) = 5x^4 + 9x^2 – 10\) |
| 4. \(f(x) = e^x \cdot x^2\) | \(f'(x) = e^x (x^2 + 2x)\) |
| 5. \(f(x) = 3e^x (2x + 1)\) | \(f'(x) = 3e^x (2x + 3)\) |
| 6. \(f(x) = x^4 e^x\) | \(f'(x) = e^x x^3 (x + 4)\) |
| 7. \(f(x) = x^3 \ln x\) | \(f'(x) = x^2 (3\ln x + 1)\) |
| 8. \(f(x) = (2x + 5)\ln x\) | \(f'(x) = 2\ln x + 2 + \frac{5}{x}\) |
| 9. \(f(x) = \sqrt{x} (x^2 + 1)\) | \(f'(x) = \frac{5x^2 + 1}{2\sqrt{x}}\) |
| 10. \(f(x) = (x + 3)\sqrt{x}\) | \(f'(x) = \frac{3(x + 1)}{2\sqrt{x}}\) |
| 11. \(f(x) = \frac{1}{x} (x^3 – 4x)\) | \(f'(x) = 2x\) |
| 12. \(f(x) = \frac{5}{x} (2x + 7)\) | \(f'(x) = -\frac{35}{x^2}\) |
| 13. \(f(x) = e^x \ln x\) | \(f'(x) = e^x \left(\ln x + \frac{1}{x}\right)\) |
| 14. \(f(x) = (x^{-3} + 2)(x^2 – 5x)\) | \(f'(x) = -\frac{1}{x^2} + \frac{10}{x^3} + 4x – 10\) |
| 15. \(f(x) = x^{5/2} (x^{-1} + 4)\) | \(f'(x) = \frac{3}{2}\sqrt{x} + 10x^{3/2}\) |
| 16. \(f(x) = (x^2 + x + 1)(x^3 – x^2)\) | \(f'(x) = 5x^4 – 2x\) |
| 17. \(f(x) = (3x^4 – 2)(5x^2 + x)\) | \(f'(x) = 90x^5 + 15x^4 – 20x – 2\) |
| 18. \(f(x) = e^x (x^3 – 2x^2 + 5)\) | \(f'(x) = e^x (x^3 + x^2 – 4x + 5)\) |
| 19. \(f(x) = 2e^x (x^4 + 3x)\) | \(f'(x) = 2e^x (x^4 + 4x^3 + 3x + 3)\) |
| 20. \(f(x) = x^6 (\ln x + 2)\) | \(f'(x) = 6x^5 \ln x + 13x^5\) |
| 21. \(f(x) = (x + 2)(x^2 – 3x + 4)\) | \(f'(x) = 3x^2 – 2x – 2\) |
| 22. \(f(x) = e^x (x^2 \ln x)\) | \(f'(x) = e^x (x^2 \ln x + 2x \ln x + x)\) |
| 23. \(f(x) = x^{1/3} (2x^2 + x)\) | \(f'(x) = \frac{14}{3}x^{4/3} + \frac{4}{3}x^{1/3}\) |
| 24. \(f(x) = (x^{-1} + 4)(x^2 – 5x)\) | \(f'(x) = 8x – 19\) |
| 25. \(f(x) = (x^2 – 3x + 1)(x^4 + 2x)\) | \(f'(x) = 6x^5 – 15x^4 + 4x^3 + 6x^2 – 12x + 2\) |
| 26. \(f(x) = (5x^3 – 2x)e^x\) | \(f'(x) = e^x (5x^3 + 15x^2 – 2x – 2)\) |
| 27. \(f(x) = (x^4 + 7)\ln x\) | \(f'(x) = 4x^3 \ln x + x^3 + \frac{7}{x}\) |
| 28. \(f(x) = (x^{-2} + 3x)(4x^3 – 1)\) | \(f'(x) = 48x^3 + \frac{2}{x^3} + 1\) |
| 29. \(f(x) = (\sqrt{x} + x)(x^{-1} + 5)\) | \(f'(x) = 5 + \frac{5}{2\sqrt{x}} – \frac{1}{2x^{3/2}}\) |
| 30. \(f(x) = (x^5 – 3x^3 + 2)(x^2 + x + 1)\) | \(f'(x) = 7x^6 + 6x^5 – 10x^4 – 12x^3 – 9x^2 + 4x + 2\) |
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