Final AD Blog #4

I do not understand substitution and whatever we learned the day before the. I wasn't here and no one has explained it to me. I soooo need help on that!

Well for my last blog, I though I would talk about implicit derivatives. They are pretty simple.

Implicit derivatives deal with x's and y's. Steps:
1. take derivative of both sides
2. every time you take the derivative of y, note it with dy/dx or y^1 (which means y(prime))
3. solve for dy/dx

Simple enough right? Lets try some example problems:

1. y^3+y^2-5y-x^2= -4
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x= 0
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)= 2x
dy/dx(3y^2+2y-5)= 2x
dy/dx= 2x/(3y^2+2y-5)

2. x^2+y^2=9
2x+2y=0
2x+2y(dy/dx)=0
(dy/dx)= 2x/2y= -x/y

Now for second derivative of implicit derivatives:
After you take your first derivative, take the second derivative.
If there is a dy/dx, its derivative will be (d^2y)/(dx^2).
It is pretty much the same thing, really simple.