Trigonometric Functions - differentiation - basic expressions.
Test Yourself 1 - Solutions.
Differentiate each of the following with respect to x unless indicated otherwise. Express your answers in the nicest possible way :)
Simple differentiation | 1. y = 5 + 2sin 3x - 4cos 5x
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2. y = 3sin 8x
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3. y = sec x | 4. Differentiate y = sin π with respect to x.
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5. | 6. | |
7. | 8. | |
Chain rule | 9. y = (tan 3x)2
y' = 2(tan 3x)1 × sec2 3x × 3 = 6 tan 3x sec2 3x |
10. y = sec2 x |
11. y = (cos x + sin 2x)3
y' = 2(cos x + sin 2x)2 × (-sin x + cos 2x × 2) = 2(cos x + sin2x)2(2cos2x - sinx) |
12. y = (2 - cos 2x)2
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13. | 14. | |
Product rule. | 15. | 16. |
17. | 18. | |
19. | 20. " express in the simplest factored form". | |
Quotient rule. | 21. | 22. |
23. | 24. Differentiate | |
25. Differentiate . | 26. Differentiate . |