1. Implicit Differentiation
Explicit vs. Implicit
The function is “implied” by an equation. You can’t separate the variables.
The function can be expressed as an equation in terms of one variable
Difficult to express y in terms of x

2. variables agree, use Power Rule
variables don’t agree, must use Chain Rule
For Example:

3. Let’s look closer at this:
Chain Rule:
Need to rename some things
Let
Then
The Chain Rule becomes:

4. So, every term with a ‘y’ in it will include the dy/dx term.
Differentiate with respect to x
Power Rule
Power Rule
Chain Rule

5. Now solve for dy/dx
Move all terms with dy/dx to one side, then factor.
Now isolate dy/dx
Notice the derivative contains both x and y