Blog 5

Were still on chapter two and each section gets a little harder. I thought it was pretty easy until we got to the product rule mixes into the chain rule. Anyways, I will explain chain rule because I understand it okay. The formula for the chain rule is f’(g(x)) x g’(x). –Derivative outside, recopy inside, times derivative of inside. d/dx= [f(g(x)] **The chain rule can also be called the general power rule.
In order to be able to do these problems you need to understand what is the outer and inner of the problem (I have a hard time with this myself.) The first few exercises of our homework problems were like this.

A few examples of identifying outer and inner:
y=(5x-8)^4 The outer would be y=u^4, and the inner would be u=5x-8
Y=csc^3x The outer would be y=u^3, the inner would be u=csc x

Now and example using the chain rule:
Y=tan^2x
-First thing you do is bring the exponent to the front (General Power Rule)
2 tan x
-Then you have to multiply it by the derivative of tan
2 tan x x (sec^2x)
The answer would be 2 tanxsec^2x

Something that I didn’t really understand was the word problems. I understand which ones are velocity, and average velocity, and I understand what you have to do to them. I just don’t get the complicated and more detailed ones. Like when something drops on impact, or when you have to plug in zero to the problem.