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| Questions | Answers |
|---|---|
| 1. \(f(x) = x^2\) | \({f'(x) = 2x}\) |
| 2. \(f(x) = 4x^3\) | \({f'(x) = 12x^2}\) |
| 3. \(f(x) = 2x^5 – 3x^2 + 6\) | \({f'(x) = 10x^4 – 6x}\) |
| 4. \(f(x) = x^4 + x^3 + x^2 + x + 1\) | \({f'(x) = 4x^3 + 3x^2 + 2x + 1}\) |
| 5. \(f(x) = 5x^4 – 2x^3 + \frac{7}{2}x^2 – x + 9\) | \({f'(x) = 20x^3 – 6x^2 + 7x – 1}\) |
| 6. \(f(x) = 5x^7 – 3x^4 + 9x\) | \({f'(x) = 35x^6 – 12x^3 + 9}\) |
| 7. \(f(x) = -7x^3 + 2x^2 – 5x + 4\) | \({f'(x) = -21x^2 + 4x – 5}\) |
| 8. \(f(x) = 6x^5\) | \({f'(x) = 30x^4}\) |
| 9. \(f(x) = \frac{1}{2}x^6 – \frac{1}{3}x^3 + \frac{1}{4}x\) | \({f'(x) = 3x^5 – x^2 + \frac{1}{4}}\) |
| 10. \(f(x) = x^3 – 4x^2 + 5x\) | \({f'(x) = 3x^2 – 8x + 5}\) |
| 11. \(f(x) = 10x^{10} + 0.5x^5\) | \({f'(x) = 100x^9 + 2.5x^4}\) |
| 12. \(f(x) = \frac{1}{3}x^5 + 2x^4 – \frac{3}{4}x^3 + x – 4\) | \({f'(x) = \frac{5}{3}x^4 + 8x^3 – \frac{9}{4}x^2 + 1}\) |
| 13. \(f(x) = 4x^8 – 3x^5 + 2x^3 – x\) | \({f'(x) = 32x^7 – 15x^4 + 6x^2 – 1}\) |
| 14. \(f(x) = 9x^8\) | \({f'(x) = 72x^7}\) |
| 15. \(f(x) = -x^3 + 5x – 7\) | \({f'(x) = -3x^2 + 5}\) |
| 16. \(f(x) = 2x^5 + 3x^4 – x^2 + 9\) | \({f'(x) = 10x^4 + 12x^3 – 2x}\) |
| 17. \(f(x) = 6x^7 – 3.5x^5 + 8x^4 – 2x^2 + 5\) | \({f'(x) = 42x^6 – 17.5x^4 + 32x^3 – 4x}\) |
| 18. \(f(x) = 7\) | \({f'(x) = 0}\) |
| 19. \(f(x) = 0.25x^4 – 1.5x^2 + 6x\) | \({f'(x) = x^3 – 3x + 6}\) |
| 20. \(f(x) = -4x^6 + 3x^3 – 9x + 2\) | \({f'(x) = -24x^5 + 9x^2 – 9}\) |
| 21. \(f(x) = x^6 + 4x^3 – 2x + 5\) | \( {f'(x) = 6x^5 + 12x^2 – 2}\) |
| 22. \(f(x) = 0.5x^8 + 1.2x^5 – 7x^3 + 4x\) | \({f'(x) = 4x^7 + 6x^4 – 21x^2 + 4}\) |
| 23. \(f(x) = -5x^4 + 10x^2 – 3\) | \({f'(x) = -20x^3 + 20x}\) |
| 24. \(f(x) = x^9 – x^6 + x^3 – 1\) | \({f'(x) = 9x^8 – 6x^5 + 3x^2}\) |
| 25. \(f(x) = 6x^4 – 12x^3 + 3x\) | \({f'(x) = 24x^3 – 36x^2 + 3}\) |
| 26. \(f(x) = 10x^9 – \frac{5}{2}x^6 + 3x^4 – x\) | \({f'(x) = 90x^8 – 15x^5 + 12x^3 – 1}\) |
| 27. \(f(x) = 4x^7 – 5x^4 + 2x^3 – 8\) | \({f'(x) = 28x^6 – 20x^3 + 6x^2}\) |
| 28. \(f(x) = x^{10} – 4x^7 + 6x^5 – \frac{8}{3}x^2 + 3\) | \({f'(x) = 10x^9 – 28x^6 + 30x^4 – \frac{16}{3}x}\) |
| 29. \(f(x) = \frac{1}{4}x^8 – \frac{3}{2}x^5 + 7x\) | \({f'(x) = 2x^7 – \frac{15}{2}x^4 + 7}\) |
| 30. \(f(x) = -2x^5 + 9x^3 – 3x^2 + \frac{1}{2}x – 7\) | \({f'(x) = -10x^4 + 27x^2 – 6x + \frac{1}{2}}\) |