Differentiate with respect to x the following functions :

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

37. 38. 39.

40.

41. if find .

42. if find

43. Show that if . then

44. if , find

45. if show that

46. if express z as an explicit function of x. Verify for these functions the formula for the derivative of a function of a function.

47. if , find the value of f(0) + a.f'(0) .

48. Find the derivative of (i) with respect to x (ii) with respect to u where .