This week we learned how to do derivatives of logarithmic functions and exponential functions. At first I was nervous to learn another element of derivatives, but I was relieved to discover that the derivatives of logarithmic and exponential functions are actually incredibly easy. It is really helpful to have a nice section in a chapter where I don't really struggle much and I finish an assignment with barely any questions. In this chapter though, there were a few sections where I struggled with the homework a lot and came to school the next day with a ton of questions. I think one of the most difficult sections for me in this chapter was the derivatives of inverse trig functions. This section was hard for me because they are the most difficult problems to simplify. For example, when you do a problem and it ends up like this: -6t/t^4(1-9/t^4)^1/2. I am pretty sure there are ways you can simplify this, but it is hard for me to figure them out. And with problems like csc^-1(x/2), there are absolute value signs on the bottom and then it just looks really ugly.
On the most recent math quiz, I messed up one of the chain rule problems. I realize now why I messed it up. The question was f(x)=sin^2[(2x-1)^4] and you had to find f'(x). I did not realize that when you have sin^2 and you use the chain rule on it, you cannot just put 2sincos. Instead, you have to separate the sin and the cos and put them in front of the inside. This makes the answer completely different than what I got. I understand it now though!
One section that I understood quite well in chapter three was actually u substitution. I liked this section because it was simple, but also kind of complicated at the same time. I think that figuring out the u and substituting helps me to understand the process of finding f(x) a lot better. And I make sure to remember the plus c's!
This will be me on Monday:
On the most recent math quiz, I messed up one of the chain rule problems. I realize now why I messed it up. The question was f(x)=sin^2[(2x-1)^4] and you had to find f'(x). I did not realize that when you have sin^2 and you use the chain rule on it, you cannot just put 2sincos. Instead, you have to separate the sin and the cos and put them in front of the inside. This makes the answer completely different than what I got. I understand it now though!
One section that I understood quite well in chapter three was actually u substitution. I liked this section because it was simple, but also kind of complicated at the same time. I think that figuring out the u and substituting helps me to understand the process of finding f(x) a lot better. And I make sure to remember the plus c's!
This will be me on Monday: