After completing this section, students should be able to do the following.

- Implicitly differentiate expression.
- Find the equation of the tangent line for curves that are not plots of functions.
- Understand how changing the variable changes how we take the derivative.
- Understand the derivatives of functions that are not defined explicitly in terms of an independent variable .
- Explain the formula for the derivative of the natural log function.
- Calculate derivatives of logs in any base.
- Calculate the derivative of an exponential function, , where .