The Chain Rule: Part 1

The Chain Rule: Part 1

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  • Pre-Calculus Begins
  • The Chain Rule The Chain Rule is much like the product and power rule, except that it deals with differentiating compositions of functions.  Formula for the Chain Rule F(x) = f(g(x)) F'(x) = f'(g(x)) * g'(x)
  • This is the Chain Rule you guys, copy down the formula, and you should get it. 
  • Hm... She doesn't look mad, I think she knows the Chain Rule
  • Pre-Calculus Ends
  • It's too early for this
  • I don't get this, it's so annoying
  • I know! 
  • Approaching The Genius
  • Thank you so much! I hope I'm not being a hassle
  • Hello, I was wondering if you could help me with the Chain Rule?
  • Oh, sure, of course I can. It's really easy. 
  • Don't worry about it, I can teach it easier than that new teacher
  • Class starts, and based on the reactions of everybody in the class, the students are struggling to keep up with their new teacher, Mr. Miteracqua. Nobody asks any questions. 
  • Learning Chain Method
  • F(x) = f(g(x)) F'(x( = f'(g(x)) * g'(x) Basically, you use the Chain Method for composite functions. For example: F(x) = 2(3x2+ 5x)3 You find the derivative of the inside of the parenthesis first, and then multiply that to the outside. Basically think of (3x2+ 5x) as just x
  • Class ends, and the students respond to their morning lesson in a negative way. A student, Ryan, notices everybody's conflicted faces, and he looks to Stephana, who doesn't seem bothered at all. He realizes that she probably understood this topic
  • Using an Example
  • F(x) = 2(3x2+5x)3 Derivative of (3x2+5x) = (6x + 5) Derivative of outside 
  • Ryan approaches Stephana, with the goal of obtaining a tutor that can help him with this difficult topic.
  • Solving the Example
  • F(x) = 2(3x2+5x)3 Derivative of (3x2+5x) = (6x + 5) Derivative of outside = Derivative of 2(x)3= 6(x)2 (6x + 5) * 6(3x2+5x)2
  • Right, okay, it should be easy since I already understand how to find the derivative of a number
  • Ryan understands the power rule, and he knows how to find the derivative of a number. Stephana tells him that it's easier to learn through example, which is what Ryan will do.
  • Okay, so first you have to understand this formula. You can't just write it down and expect to remember it. You need examples.
  • Ryan finds himself confused as to how to find the derivative of the second part of the chain rule, "the outside". Stephana tells him how to rewrite the problem, and it seems Ryan understands. 
  • Wait a second... This makes absolutely no sense. I don't get how to find the derivative of the outside, or what that even means?
  • Oh, I see it now, I know what you're saying. Let me see if I can do it.
  • Hehehe. So just think of the parenthesis as an x. So basically, rewrite the "derivative of outside" as 2(x)3, and then find the derivative of that
  • Ryan solved the problem, and with that one single example, Ryan understood the Chain Rule, and was ready for anything that would come his way.
  • Ayyy, thank you so much! You've been a great help! 
  • That's it, good job
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