11. Implicit Differentiation

Implicit differentiation exists to allow us to take the derivative of non-functions like circles or other crazy looking things. When looking at an equation, you can tell it is not a function if you cannot isolate y with only one equation.

I strongly encourage students to use dy/dx as opposed to y' in this section to avoid mixing up y and y'. Another important tip is that any time y is multiplied by x, the product rule will be required to take the derivative of this.

Basic Steps:

1. Take the derivative with respect to x. Use the product rule any time x is multiplied by y.

2. Get all the dy/dx terms on one side and all of the other terms on the other side

3. Factor dy/dx out of all the terms on that side

4. Divide both sides by the factored term to solve for dy/dx

Example Problem 1: (This problem follows the steps above exactly)

Example Problem 2:

I color coded the derivative step to make it easier to make it easier to tell where the product rule parts came from.

Practice Worksheet:

For more information and some easier practice problems :) Check here:

Khan Academy Quiz #1