The second exam will cover chapters 4, 5.5, 5.1-5.3. You should review your homework, discussion sheets, class notes, and the textbook. Some test problems will be like quiz problems while some may be harder than quiz problems. The test will involve calculations as well as writing sentences to explain an idea or interpret a result. Below is a list of topics.

• Definition of derivative
  • understand the definition of derivative, including using it to find derivatives
  • understand what derivatives are and how their meaning relates to the technical definition
• Know basic rules for taking derivatives, and be able to evaluate derivatives using these rules.
  • power rule
  • product rule
  • quotient rule
  • chain rule
  • derivative of exponential
  • derivative of ln
  • derivative of sine and cosine
  • word problems like those on discussion sheets involving applying rules using given values
• Using the chain rule
  • implicit differentiation
  • derivatives of inverses
  • logarithmic differentiation
• Applications of derivatives
  • related rate problems
  • linear approximation and tangent lines
  • error propagation
  • differential equations, especially related to exponential growth (end of 4.6)
  • applying L'Hospital's rule
• Using derivatives to understand functions
  • Identify local and global extrema
  • Identify inflection points
  • Identify where functions are increasing/decreasing and concave up/down
  • Using information about the first and second derivatives to understand function behavior and generate graphs.
  • Estimating derivatives from graphs, as on discussion sheets