This week's lessons are based on "u" substitution for integration, implicit differentiation, and higher order derivatives. The one I had the most trouble with was implicit differentiation. As you solve for the derivative, the work just looks so ugly that I just don't want to look at it. It also takes super long, and I'm pretty lazy with it. It wasn't hard solving it though. All I had to do was just differentiate everything, which wasn't that hard.
The integration was a lot easier, mainly by the virtue that it looked a lot cleaner. I didn't really have a lot of trouble with that one. I was a little weirded out by the part where we pulled u out to take the derivative since it kind of did its own thing apart from the function, but then I realized that it's just derivatives and substitution, so I felt a lot better about that.
Lastly, we looked at higher order derivatives for implicit differentiation. That is, taking the derivative of a derivative, turning dy/dx into (d^2y)/(dx^2). It's pretty much just the product or the quotient rule again, but the part that wowed most people in the class was the part where we substituted the derivative for the derivative we solved. I have to admit though, that was pretty spiffy.
The integration was a lot easier, mainly by the virtue that it looked a lot cleaner. I didn't really have a lot of trouble with that one. I was a little weirded out by the part where we pulled u out to take the derivative since it kind of did its own thing apart from the function, but then I realized that it's just derivatives and substitution, so I felt a lot better about that.
Lastly, we looked at higher order derivatives for implicit differentiation. That is, taking the derivative of a derivative, turning dy/dx into (d^2y)/(dx^2). It's pretty much just the product or the quotient rule again, but the part that wowed most people in the class was the part where we substituted the derivative for the derivative we solved. I have to admit though, that was pretty spiffy.