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

  • Compute directional derivatives.
  • Use the directional derivative to show that the gradient vector points in the initial direction of greatest increase for the function.
  • View the chain rule in terms of the gradient.
  • Compute the derivative of the composition of a function of several variables with a vector-valued function.
  • Use the chain rule of several variables to implicitly differentiate a curve.