Week 9

Finally, the first nine weeks are over. This week, we reviewed for our exam on Monday and Tuesday. On Wednesday, we took our multiple-choice exam, and on Thursday, we took our free response test. On Friday we learned something new: Implicit Derivatives.
I get Implicit Derivatives. They are basically just like regular derivatives, except they have a few extra steps. They must involve two constants (a x and a y) to be considered Implicit.
Steps:
Take the derivative like normal of both sides.
Every time you take the derivative of y – note it with dy/dx or y’.
Solve for dy/dx.
Example: y^2 + 5y = x^2
2y + 5 = 2x
Just took regular derivative like y was an x.
2y(y’) + 5(y’) = 2x
Notes y’ everywhere I took the derivative of y.
y’ = 2x/(2y+5)
Factored out y’ and divided (2y+5) over.
　
　
I also think I’m pretty good at finding the equation of a tangent line.
Steps:
Take f ‘(x).
Plug in x to find your slope: m.
Plug x into f(x) to find y (if not already given).
Using m and (x,y), plug it into slope-intercept form: (y-y1) = m(x-x1).
I feel pretty confident, so I’m going to go out on a limb and say I don’t not understand anything that I can think of right now. But, I’m am getting ready for a long three MORE nine weeks.