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  • Learning the Chain Rule Story
  • Pre-Calculus Class
  • If f(u) is a differentiable function of u and u=g(x) is a differentiable function of x, then y =f(g(x)) is a differentiable function of x and
  • Good Job class! We'll have a quiz on this tomorrow.
  • The Chain Rule 
  • dy/dx = dy/du × du/dx
  • Lunch
  • Don't worry Chloe, I'll tutor you during Study Hall!
  • The Chain Rule 
  • dy/dx = dy/du × du/dx
  • Omg, we have a quiz on the Chain Rule ! I don't understand it, can you help me?
  • Maybe I can help too!
  • This is the story of a student from Riverside High school, named Chloe, who struggles with the Chain Rule. Enjoy!
  • Study Hall
  • The Power Rule Before solving the problem it looks like this: f(x)=xn When you find the derivative it looks like this : f'(x)=n*x(n-1)
  • After Mr. C teaches the Chain Rule, Chloe doesn't understand the lesson. Even though Mr. C asks for any questions, she is ashamed to reveal her struggle.
  • Study Hall
  • f(x)=3x5
  • You don't write f'(x) for your second step because you're only showing your work, you didn't find the derivative yet!
  • Example
  • f(x)=3*5(5-1)
  • f'(x)=15x4
  • During Lunch, Chloe asks her best friend, Essence, for help and Tj offered to help as well.
  • Study Hall
  • Keep the inside of the parenthesis the same. Think of it as 'x' it doesn't change
  • f'(x)=4(x3+3x)3(3x2+3)
  • f(x)=(x3+3x)4
  • Now you take the derivative of what's inside the parenthesis and multiply it
  • Essence proceeds to explain that you multiply the exponent (n) by the coefficient in front of 'x'. Remember: if you don't see no coefficient in front of x, then it's 1. Then, essence explains that 'n' in the equation is the exponent and when finding the derivative you always subtract the exponent (n) by 1, so (n-1).
  • In order to understand the Chain Rule better, you'd have to be familiar with the Power Rule.
  • definitely.
  • Tj then elaborates on the Power Rule, by providing an example. He multiplied the coefficient (3) by the exponent (5) and then subtracted the exponent by 1 so, (5-1).
  • Ohhh, I get it !
  • Here's an example!
  • Essence thoroughly explains an example of the Chain Rule. She says that you treat the problem similarly to a Power Rule one. Keep what's inside the parenthesis and simply multiply the coefficient by the exponent and then subtract that exponent by one (4-1).
  • Now that you understand the Power Rule, you can do the Chain Rule! They're similar. 
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