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Our class lesson on the chain rule

Our class lesson on the chain rule

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    Scribe 2 Scribe 2 Presentation Transcript

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