Calculus - Differentiation - Basic techniques.
Test Yourself 1.
Find the gradient function of the following functions - that is "differentiate each of the following functions" with respect to the given variable. All questions use only the direct technique as described - no special rules.
As always - your first step is to look at the structure and decide what you need to do.
The questions below focus on the structures of: |
1. the basic format. |
2. the use of simple brackets. |
3. the use of the d/dx format. |
4. radicals. |
5. terms in the denominator. |
6. fractions with only one term in the denominator. |
1. Basic format. | 1. y = x3 + x
Answer.3x2 + 1. |
2. y = 3x3 + 2x2 - x - 42 | 3. y = 4x2 + 5x |
4. y = 3t - 5t2 | 5. y = 0.5x4 + 1.5x2 - 42 | 6. y = x2.5 |
|
2. Simple brackets. | 7. s = 2t2(3t + 4) | 8. m = 4n3(n5 + 3n - 1) | 9. y = 3x3(2x4 - 5x2 - x) |
3. Use of d/dx format. | 10. | 11. | 12. |
13. | 14. | 15. | |
4. Radicals. | 16. | 17. | 18. |
(see the Solutions for the answers to Q 18 - 21). | 19. | 20. | 21. |
5. terms in the denominator - so the neeed to use negative signs. | 22. | 23. | 24. |
25. | 26. | 27. | |
6. Fractions with 1 term in the denominator. | 28.
Hint.How many terms in the denominator? ONE. So divide each term in the numerator by the term in the denominator and then differentiate normally. |
29. | 30. |