This week in APCalc, we learned about u substitution. U substitution is an easier way to think about doing the Chain Rule. It's easier because you can replace the inside of a function with a variable, then just plug that part of the equation back in where the variable is. I find this useful in more complex equations, but I do not think I need to do it on every problem. It is definitely very useful on problems that have to do a double derivative problem. This is easier because it cleans up a lot of the numbers and replaces it with variables, making the work easier since everything is less cluttered. We also learned about finding the derivative with respect to y when it is not a simple y= problem. You have to take the derivative of each side, using derivative rules when needed. Then you do algebra to get all of the dy/dx's on the same side, then solve for dy/dx. Once you have that equation, you plug in your point to find the slope. What's different about this, is that you have to plug in both x and y into the equation. These problems are the collection of everything we've learned up to this point with derivatives.
0 Comments
This week in Calc., I learned about the fabulous Chain Rule. This rule is kinda difficult to comprehend at first, but I think I understand the Chain Rule better than when we first started that worksheet. The Chain Rule applies to when you have composite functions, or functions inside of functions. To use the Chain Rule, you take the derivative of the outside functions, but keep the inside function the same, and multiply it by the derivative of the inside function or you could use the equation, f(g(x))=f'(g(x)) x g'(x). The Chain Rule took me some time to get used to and I think it will take me a little longer to understand the more complex problems, but I have the general idea down. The problems I have trouble with are the ones that are when you have to chain the Chain Rule. Luckily, there are several people I know in the class that can help me solidify it. I found it quite cool that we have already been doing the Chain Rule when we do the Power Rule. I’m glad that we learned the Power Rule before the Chain Rule because it is so much shorter than doing the Chain Rule on a simple equation.
This week in Calculus, we learned the rules for derivatives and an easier way find the derivative. I really wish we learned this trick earlier when we first learned derivatives because it would have saved me so much time and paper. Derivatives have become less terrifying and scary now that we've been doing it on a consistent basis, but then you threw in those anti-derivatives. They are not difficult but when you first said anti-derivatives, I thought, "Dear lord, what the heck is an anti-derivative!" I have since found out that they are not as scary as I originally thought, but if you had taught them on Friday, which was Friday the 13 in the scariest month ever, October, I probably would have thought they were the most terrifying, evil, most difficult thing to do. The only difficult thing about anti-derivatives is remembering to add the +c at the end. Derivatives are easy now that we've had lots of practice on them. I think they're starting to be fun. What have you done to me, calculus shouldn't be fun! I hope the rest of the chapters in this trimester, and the rest of the trimesters this year are just as easy and kinda fun, but not too fun because calculus shouln't be fun.
|
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
February 2018
Categories |