This week has been a trip. I really don't mind the chain rule and all, but I feel like there are so many gray areas or holes in it that is hard to determine when you are supposed to what sometimes. For example, the first question of the quiz. It took me a while to figure out because I did not know whether you could take the derivative of something and just square it if what you are trying to find the derivative of is squared. Then I wasn't sure whether you were supposed to apply the chain rule to the thing, let's say sin^2. If you were, then you would put a 2 out in front and multiply by the inside. If you could just square the derivative of sin, you would get something completely different. I feel that it is little things like that that confuse me. Another thing that can confuse me with the chain rule is how to know how many inside functions there are. For example, on the quiz, there was a question like cos square root 3x. I realized that you have to raise the 3x to the 1/2 power. So then I found the derivative of cos and put it in front of the inside (3x), then multiplied by the derivative of the inside. But I did not realize that there was even another inside function, 3x. This would make the problem have a x 3 at the end, which I did not have.
I feel like I understand u substitution quite well, maybe even more than the chain rule. The only thing that can get confusing is what to call the u. This is especially confusing when there are addition and subtraction signs in the problem. I think I came to the conclusion that most of these problems with have the same inside function in both parts, therefore making the u just that part.
Thursday we started learning about implicit differentiation. I understand this part of derivatives quite well. The only gray area for these types of problems is the fact that they usually involve many, many variables, and a lot of them are very similar, which makes it very easy to make simple mistakes. For example, there was a problem that we did that looked a little like this:
2x(x-y)^2=x=xdy/dx-y-ydy/dx+x-y+xdy/dx+ydy/dx ......... and that is just a handful. BUT, the fun thing is, a lot of that cancels out so it's all good.
I feel like I understand u substitution quite well, maybe even more than the chain rule. The only thing that can get confusing is what to call the u. This is especially confusing when there are addition and subtraction signs in the problem. I think I came to the conclusion that most of these problems with have the same inside function in both parts, therefore making the u just that part.
Thursday we started learning about implicit differentiation. I understand this part of derivatives quite well. The only gray area for these types of problems is the fact that they usually involve many, many variables, and a lot of them are very similar, which makes it very easy to make simple mistakes. For example, there was a problem that we did that looked a little like this:
2x(x-y)^2=x=xdy/dx-y-ydy/dx+x-y+xdy/dx+ydy/dx ......... and that is just a handful. BUT, the fun thing is, a lot of that cancels out so it's all good.