September 8 - The Chain Rule

The Chain Rule is the rule for the composition of functions - that is one function is "inside" another, ie f(x) = a(b(x)). The Chain Rule is an all encompassing rule - you have already been using it though it hasn't been apparent.

The thought process for using the Chain Rule is to think

"The derivative of f(x) will be the derivative of the outside function times the derivative of the inside function."

The trick is that when you differentiate the "outside function," you don't change the function on the inside. That probably doesn't make sense to read, but ultimately, with practice, I think you will come to understand.

Notes from today are shown below and include several worked examples.