Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/14

1.  
2. CHAPTER IV
   

   DIFFERENTIATION

3. SECTION

   PAGE

4. 25.

   Introduction ................................................................................................................................................................................................................................................................................................................................................................................................

   25

5. 26.

   Increments ................................................................................................................................................................................................................................................................................................................................................................................................

   25

6. 27.

   Comparison of increments ................................................................................................................................................................................................................................................................................................................................................................................................

   26

7. 28.

   Derivative of a function of one variable ................................................................................................................................................................................................................................................................................................................................................................................................

   27

8. 29.

   Symbols for derivatives ................................................................................................................................................................................................................................................................................................................................................................................................

   28

9. 30.

   Differentiable functions ................................................................................................................................................................................................................................................................................................................................................................................................

   29

10. 31.

    General rule for differentiation ................................................................................................................................................................................................................................................................................................................................................................................................

    29

11. 32.

    Applications of the derivative to Geometry ................................................................................................................................................................................................................................................................................................................................................................................................

    31

12.  

    CHAPTER V
    RULES FOR DIFFERENTIATING STANDARD ELEMENTARY FORMS

13. 33.

    Importance of General Rule ................................................................................................................................................................................................................................................................................................................................................................................................

    34

14. 34.

    Differentiation of a constant ................................................................................................................................................................................................................................................................................................................................................................................................

    36

15. 35.

    Differentiation of a variable with respect to itself ................................................................................................................................................................................................................................................................................................................................................................................................

    37

16. 36.

    Differentiation of a sum ................................................................................................................................................................................................................................................................................................................................................................................................

    37

17. 37.

    Differentiation of the product of a constant and a function ................................................................................................................................................................................................................................................................................................................................................................................................

    37

18. 38.

    Differentiation of the product of two functions ................................................................................................................................................................................................................................................................................................................................................................................................

    38

19. 39.

    Differentiation of the product of any finite number of functions ................................................................................................................................................................................................................................................................................................................................................................................................

    38

20. 40.

    Differentiation of a function with a constant exponent ................................................................................................................................................................................................................................................................................................................................................................................................

    39

21. 41.

    Differentiation of a quotient ................................................................................................................................................................................................................................................................................................................................................................................................

    40

22. 42.

    Differentiation of a function of a function ................................................................................................................................................................................................................................................................................................................................................................................................

    44

23. 43.

    Differentiation of inverse functions ................................................................................................................................................................................................................................................................................................................................................................................................

    45

24. 44.

    Differentiation of a logarithm ................................................................................................................................................................................................................................................................................................................................................................................................

    46

25. 45.

    Differentiation of the simple exponential function ................................................................................................................................................................................................................................................................................................................................................................................................

    48

26. 46.

    Differentiation of the general exponential function ................................................................................................................................................................................................................................................................................................................................................................................................

    49

27. 47.

    Logarithmic differentiation ................................................................................................................................................................................................................................................................................................................................................................................................

    50

28. 48.

    Differentiation of $\scriptstyle {\sin v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    54

29. 49.

    Differentiation of $\scriptstyle {\cos v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    55

30. 50.

    Differentiation of $\scriptstyle {\tan v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    56

31. 51.

    Differentiation of $\scriptstyle {\cot v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    56

32. 52.

    Differentiation of $\scriptstyle {\sec v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    56

33. 53.

    Differentiation of $\scriptstyle {\csc v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    57

34. 54.

    Differentiation of $\scriptstyle {\operatorname {vers} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    57

35. 55.

    Differentiation of $\scriptstyle {\operatorname {arc~sin} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    61

36. 56.

    Differentiation of $\scriptstyle {\operatorname {arc~cos} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    62

37. 57.

    Differentiation of $\scriptstyle {\operatorname {arc~tan} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    62

38. 58.

    Differentiation of $\scriptstyle {\operatorname {arc~cot} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    63

39. 59.

    Differentiation of $\scriptstyle {\operatorname {arc~sec} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    63

40. 60.

    Differentiation of $\scriptstyle {\operatorname {arc~csc} v}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    64