This week was mostly a review on how to solve problems when we have implicit derivatives, explicit derivatives and a second derivative in an implicit function. To solve for an implicit derivative and a explicit derivative you have to know the difference. An implicit derivative is not solved for y and an explicit derivative is solved for y. when your solving for either the implicit or explicit derivatives after you take the derivative of something with a y you have to put the dy/dx notation behind it.

Here are the steps you need to solve for an implicit derivative:

1) Differentiate both sides with respect to x. d_/dx
2) Collect all dy/dx terms on one side, and move the other terms to the other side.
3) Factor out dy/dx.
4) Solve for dy/dx.
5) Simplify, and replace with original equation if possible

Example: x^3 + y^3 = 64
3x^2 + 3y^2dy/dx = 0
3y^2dy/dx = -3x^2
dy/dx = -3x^2/3y^2
= -x^2/y^2