This week in A.P. Calculus, we started the hardest unit that I've encountered thus far this year. That was U - Substitution. I think this unit is particularly challenging because I have a tough time using and thinking about multiple variables, not to mention anti - differentiating equations. Going through the notes, most of the material went over my head but after a few days' practice, I believe I was able to nail the bulk of the concept down. Topics that are completely unfamiliar which U-Sub is, tend to take more time to understand than topics that I have either seen before or can be worked out. There is not all that much to U - Sub to begin with, and I think that is why it can be so challenging. Really all there is to it is identifying U (which is easy) taking the derivative of U, messing with the original function to make it look nice, and then inputting the original equation back in for the evaluated U. There are lots of variations to this process, all messing with any set rules that can be used to solve the problem. With any difficult problem, I think the best approach is to attack it from multiple directions and multiple angles, if at all possible.
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This week in A.P. Calculus, we focused our attention toward taking derivatives of regular functions and composite functions. These two topics are not all that hard for me to understand. For most of the functions you can just follow the chain rule or follow basic rules of algebra to get to the bottom of a problem. Years from now I'm not sure I will remember rules like the product rule or quotient rule but I think it is extremely helpful to understand the process of taking a derivative, for which reasons I am a little unsure of. One thing that I do know that I can get out of learning this material is continuing to build my critical thinking skills. That is one of the things math has done for me, and I am forever grateful for that.
The toughest part of this unit (so far) is deriving composite functions. Functions inside of one another have always been super hard to picture in my head and separate and solve. It usually helps if there is a systematic method to solve those functions like a set of rules to follow to get to the bottom of the problem and come up with a solution. Other than that, I feel like I am doing just fine. Peace, love, and prosperity.
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