Logarithmic functions - Differentiation - basic techniques.
Test Yourself 1.
The questions on this page focus on differentiating:
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Differentiate each of the following:
Basic structure | 1. y = ln (3x-2) | 2. y = loge(6x2 - 3) |
3. Find f '(e) if
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4. y = loge (1 - 3x2) | |
5. y = loge 2ex | 6. . | |
Chain rule | 7. | 8. |
9. y = [ln (2x - 1)]3 | 10. y = loge (loge ex) | |
Product rule | 11. Show that the derivative of
x[(logex)2 - 2 logex + 2] = [logex]2 |
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12. y = x lnx | 13. y = 4x2 ln (2 - x) | |
14. y = 2x3 loge (3x - 7) | 15. (x2 - 5)ln(3 - x2) | |
16. Determine the range of values of x where the curve
y = x2 ln x is concave up. |
17. Determine the range of values for which the curve has a negative gradient.
Answer correct to 3 decimal places. Answer.0 < x < 0.607. |
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Quotient rule | 18. . | 19. |
20. | 21. | |
Use log laws | 22. y = loge105x+2. | 23. y = 7ln (4 - 2x)3 |
24. y = 3ln [(2x - 1)(3x + 2)] | 25. y = 10ln [(x + 3)2(5x - 2)3] | |
26. | 27. | |
28. | 29. | |
30. y = log2x | 31. y = x2 log2x a |