Implicit Differentiation and Related Rates
Introduction
Implicit Differentiation is a way of taking derivatives of equations where the x and y are mingled on the same side of an equation. It is done by treating each as independent variables where the derivative of x is 1(dx) as would be y. Another example is the derivative of y³ would be 3y²(dy). The equation is then manipulated to leave 
on one side of the equals sign and an expression containing x and y on the other side.
A related rate is determining how one variable is affected by a change in another variable. Often related rates are solved in respect to time.
For example:
1.1 Finding the derivative of a circle: 
= 
= 
Since you have the original equation, you can easily find the slope at any coordinate on the graph by knowing either variable.
