3.3 The Chain Rule & 3.4 The Product and Quotient Rules

Main Points:
The derivative of a composite function (f (g(t)) can be calculated as the derivative of the outside function multiplied by the derivative of the inside function (f ' (g(t)) * g ' (t)). This rule can also be used on a composite function. Just substitute the function in for g (t). The product rule states that (fg)' = f ' g + f g'. In other words, the derivative of a product is the derivative of the first times the second plus the derivative of the second times the first. The Quotient rule states that (f/g)' = f ' times g minus f times g ' all divided by g^2.

Challenges:
The first explanation of the chain rule where the book defined it in terms of dy/dt was confusing for me, I guess the form of notation that they put it in was the only part I had trouble with because I understand the concept, but it would be helpful if you went over that way of describing the chain rule in class.

Reflections:
The chain rule is really helpfull in solving derivatives, but I wonder what a graph of the function of a function and then the derivative of that would look like. I can't picture it. I wonder if you could give us a graphic sense of the chain rule in class. This class seems to be all about the why aspect of calculus, but it seems like the book glosses over the proofs for these rules.