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Tangents and Normals

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

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Tangents and Normals

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  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 = 1y = 16 Substituting

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

  4. Worksheet 2

  5. Rules of Differentiation Differentiating Trig Functions

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

  7. Exponential

  8. 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

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

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

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

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

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

  14. Differentiating logsNote: You can only differentiate natural log so any other base needs to be converted first.

  15. Examples

  16. Hard Example 1 4 3 2 4 1 3 2

  17. Product Rule

  18. Product Rule f g

  19. Product Rule

  20. Product Rule

  21. Quotient Rule

  22. Quotient Rule f g

  23. Quotient Rule

  24. Quotient Rule

  25. Quotient Rule

  26. Quotient Rule

  27. Quotient Rule

  28. When a curve is written in the formit is said to be defined explicitly.When a curve is written in the formit is said to be defined implicitly. Example:

  29. Implicit differentiation Differentiating with respect to x

  30. Implicit differentiation Differentiating with respect to x

  31. Implicit differentiation Differentiating with respect to x

  32. Implicit differentiation

  33. Implicit differentiation

  34. Parametric Equations

  35. Parametric Equations

  36. Parametric Equations

  37. Parametric Equations

  38. Example 2

  39. Second derivative

  40. Second derivative

  41. Second derivative

  42. Example 2

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