Post 10

So this past week and the Friday before that we started the second nine weeks. The first thing we learned was implicit derivatives.

Implicit derivatives are just like regular derivatives, except they involve x and y, and when you take the derivative of y, you must always note it with dy/dx or y'. After dy/dx is noted, you need to solve for dy/dx, giving you your implicit derivative.

The second thing we learned was second implicit derivatives. They are just like taking the second derivative of a normal function, except just like implicit derivatives, it involves x and y. When taking a second implicit derivative, you just take the derivative of a first implicit derivative. You note a second derivative as d^2y/dx^2. Just like in a first implicit derivative, you always need to note whenever you take the derivative of y, only in the second derivative, you're finding the second derivative, so you plug your first derivative in anywhere dy/dx is noted.

The third thing we learned this week was related rates. The steps for related rates are as follows:

1. Identify all variables and equations

2. Identify what you are looking for

3. make a sketch and label

4. Write an equation involving your variables

5. take the derivative with respect to time (dn/dt)

6. subsittute in derivative and solve.

Finally, this week we learned how to find angles of elevation. This has to be the part where I am struggling the most in. I was just trying to do my homework and I couldn't really do most of it. I did number 43 fully because it was just like one of the examples we did in class, but I got confused on the rest.

For number 44, I'm confused about what x is supposed to be or if we're supposed to find x? Also, I'm not sure if x is supposed to be 25, because where the problem says there is 25 feet of line out. It dosen't really say if the fish is right on top of the water and that is where the line ends or if there is line beneath the water? Even if I did have this information, I'm still really confused on what to do next. The same goes for numbers 45 and 54.