Oh my god I think we finally finished the derivative unit. How long has it been? 3 weeks? 4 weeks? 6 WEEKS?!?! I feel accomplished. In this time I’ve gone through, what derivatives are, how do figure out if functions are differentiable, basic rules for differentiation including exponents, product and quotient rules, derivatives in trigonometric functions, derivatives in composite functions, derivatives in exponential functions, implicit differentiation, and how to do all of it backwards. Turns out there are all sorts of little math rules and nuances that make it cool but also really, really annoying.
This week we wrapped everything up with a lesson on Implicit differentiation and derivatives of exponential functions. Implicit differentiation kind of ties everything together because it shows how to take the derivative of a function not written explicitly as y equals x. A common application of this is in circular functions where x squared plus y squared equals radius squared. Even though I was a sleepless, miserable wreck this week I feel like I still got a handle on the material really well after I actually finished my homework assignments and had time to process the information. Using the solutions manual to make sure I was doing the problems correctly helped a lot too.