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Our class lesson on the chain rule

Our class lesson on the chain rule

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Scribe 2 Presentation Transcript

  • 1. 1
  • 2. e y w da learn To ed ab out le! Ru in  a  ch he t 2
  • 3. It states: 3
  • 4. It basically tells you how to get the derivative of a function that is composed of other functions. 4
  • 5. Seems  simple enough... 5
  • 6. Well let's try it out 6
  • 7. 7
  • 8. Let's break it up into its functions 8
  • 9. 9
  • 10. Outer  function Inner function 10
  • 11. Outer  function Inner function Our rule: 11
  • 12. Outer  function Inner function Our rule: let's look at this part 12
  • 13. Outer  function Inner function Our rule: Now let's look at just this 13
  • 14. Outer  function Inner function We  Know how to work with this 14
  • 15. Outer  function Inner function Remember: is fed So 15
  • 16. Outer  function Inner function Remember: 16
  • 17. Outer  function Inner function Our rule: 17
  • 18. Outer  function Inner function Our rule: Now let's look at just this 18
  • 19. Outer  function Inner function 19
  • 20. 20
  • 21. Or just look at it using power law, a tad bit  more complicated but for some reason this  is the first that comes to my mind when I  look at these (guess I'm just odd) 21
  • 22. Outer  function Inner function 22
  • 23. Outer  function Inner function Now let's put it all together 23
  • 24. Outer  function Inner function together Now let's put it all 24
  • 25. Outer  function Inner function 25
  • 26. This will barely ever  appear on a test as an  answer to multiple  choice 26
  • 27. This might. The 7 has been  factored in and it is no  longer color coordinated. 27
  • 28. Well that  wasn't that  hard 28
  • 29. Now a bunch more  a lot faster 29
  • 30. 30
  • 31. 31
  • 32. Now we run into a  slightly different case 32
  • 33. 3 functions ! 33
  • 34. 34
  • 35. So what do we do? 35
  • 36. We use chain  rule more than  once! 36
  • 37. From what I saw this is  what I think using chain  rule more than once is: 37
  • 38. Following the pattern  for four functions: I  think  this is right 38
  • 39. Back to this then 39
  • 40. 40
  • 41. 41
  • 42. 42
  • 43. And from here it is just grant work 43