Implicitly Differentiating the World

1. Four types of graphs/functions that do not have a derivative are the horizontal line, the vertical line, the absolute value function, and the cusp graph.

Absolute Value

Vertical Line



2. During the process of implicit differentiation you are trying to find Dy/Dx. To do this you take the derivative of the function and using the necessary method and for each variable you take the derivative of you multiply by either Dx/Dx or Dy/Dx, depending of the variable. Then you get all the Dy/Dx on the same side then solve for Dy/Dx.

3. The most important thing to remember in a related rate problem is to always multiply by the proper term when you take the derivative of a variable.