Chapter 18: Functions of Several Variables

Partial Differentiation

Introduction When a function of more than one independent input variable changes in one or more of the input variables it is important to calculate the change in the function itself. If we hold all but one of the variables constant and find the rate of change of the function with respect to the remaining variable, then this process is called partial differentiation. In this Block we show how to carry out the process.


Before starting this Block you should:

outcomes Learning outcomes

After completing this Block you should:

  • understand the principle of differentiating a function of one variable
  • understand the concept of partial differentiation
  • differentiate a function partially with respect to each of its variables in turn.
  • evaluate first partial derivatives.
  • carry out two successive partial differentiations.
  • formulate second partial derivatives.

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