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 .