1. Implicit Differentiation

2. Background
In some cases it is not possible to solve an equation as a single equation
For Example:
would be solved as two equations:
and
In order to find the derivative of the function, you would have had to find the derivative of each part

3. Implicit Differentiation
Don’t need to solve an equation for y first in order to find y’
You will differentiate both sides with respect to x and solve the result for y’

4. Example
Find y’ for

5. Practice
Find y’ for:

6. Find the derivatives at the given points:

7. Find the equation of the tangent line to the function at the given point:

8. Find the second derivative
7) 8) 9)

9. Logarithmic Differentiation
Derivatives of complicated functions can be simplified by taking logarithms

10. Example
Find the derivative of