
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, $a^x$, where $a>0$.