1. Tangents and Normals
The equation of a tangent and normal takes the form of a straight line i.e.
To find the equation you need to find a value for x, y and m and then substitute to find the value of c.

2. Find the equation of the tangent to the curve y = x2 – 3x + 18 at the point (1, 16).
x = 1 y = 16
Substituting

3. To find the equation of the normal, use the perpendicular gradient i.e.

5. Worksheet 2

6. Rules of Differentiation
Differentiating Trig Functions

7. A list of the trigonometry differentials is given in your formula sheet.

9. Exponential

11. Chain Rule applies when we have a function of a function e. g
Chain Rule applies when we have a function of a function e.g. Take two functions:
Now combine them into one function by eliminating u
Function 1
Function 2

12. Chain Rule applies when we have a function of a function e. g
Chain Rule applies when we have a function of a function e.g. Take two functions:
Note:
Function 1
Function 2

13. Think of it like this:
Differentiate the first function as a whole and then differentiate what is inside of it.

14. Differentiate function 1
Think of it like this: Differentiate the first function as a whole...
Differentiate function 1

15. Think of it like this: Differentiate the first function as a whole and then differentiate what is inside of it.
Then function 2

16. Example: Function 1 Function 2 Differential of 2x + 4
Differential of sin

18. Differentiating logs Note: You can only differentiate natural log so any other base needs to be converted first.

20. Examples

21. Hard Example 1 4 3 2 4 1 3 2

22. Product Rule

23. Product Rule f g

24. Product Rule

25. Product Rule

27. Quotient Rule

28. Quotient Rule f g

29. Quotient Rule

30. Quotient Rule

31. Quotient Rule

32. Quotient Rule

33. Quotient Rule

35. When a curve is written in the form it is said to be defined explicitly. When a curve is written in the form it is said to be defined implicitly.
Example:

36. Implicit differentiation
Differentiating with respect to x

37. Implicit differentiation
Differentiating with respect to x

38. Implicit differentiation
Differentiating with respect to x

39. Implicit differentiation

40. Implicit differentiation

41. Parametric Equations

42. Parametric Equations

43. Parametric Equations

44. Parametric Equations

45. Example 2

46. Second derivative

47. Second derivative

48. Second derivative

49. Example 2