When a function is defined in terms of two variable, say *x* and *y*, you can assume one of them stays constant and see how the function changes when the other one changes. That is called taking the partial derivative.

An example might be, if a company making a product has a profit that is simultaneously a function of labor costs and material costs, sometimes it is beneficial to analyze the profit to see how the rate of change of profit varies with the changes of each of the variables separately. This could answer the question, for example,: “Assume the cost of the materials stay constant, how would the profit vary with the change in labor costs.”

The variable that is assumed to stay constant is treated like a regular constant when taking the derivative “with respect to” the other variable. See some worked out problems in the following two links to further clarify this explanation. Note the special symbol used to denote the **P**artial derivative.

partial deriv probs pg 1

partial deriv pg 2

Do the odd numbered problems for homework.

partial deriv hw 4 19 16

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