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.
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This week we continued our exploration of derivatives, again. After learning about the chain rule last week, we learned the concept of U Substitution, which I guess is the inverse of the chain rule. One undoes what the other does. The Chain rule is the formula to find the derivative of a composition function. The U rule simplifies what the Chain rule does and makes it easier to identify its parts to antiderivative a derivative.
This week I think I have finally pinpointed why I am struggling with math more so this year that I have in previous years. I am a very read to learn kind of person. Due to my generalized anxiety I have a hard time staying focussed on a lesson and usually retain read information better. In years past my math classes have often had pre prepared notes where the mathematical concepts were put into words and taught that way. This year class has been taught mostly through examples written on the board and maybe a sentence rule here or there, and then most of the information was spoken lecture style as opposed to being written out and projected. There is nothing wrong with this, I just need to rethink my note taking system to better reflect the information being spoken and note just writing what is on the board. |
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January 2018
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