Product rule

The  exercise appears under the Differential calculus Math Mission. This exercise applies the product rule from differential calculus.

Types of Problems
There are two types of problems in this exercise:


 * 1) Use the graphs to find the value of the derivative: This problem has a graph and possibly other representations of functions involved in a product. The student is expected to use the information provided to find the value of the derivative at a particular point.Prodrule1.png
 * 2) Find the value of the derivative directly: This problem provides a function that is a product. The student is expected to find the value of the derivative at a particular point.Prodrule2.png

Strategies
Knowledge of the product rule and other differentiation rules are encouraged to ensure success on this exercise.
 * 1) In function notation the chain rule is (f(x)*g(x))'=f(x)g'(x)+g(x)*f'(x).
 * 2) Because of commutativity of addition, the order of the derivatives does not matter on the product rule.
 * 3) A mnemonic is "First times the derivative of the second, plus the second times the derivative of the first.

Real-life Applications

 * 1) The derivative attempts to extend the concept of slope to objects that are not lines. It expresses a rate of change.
 * 2) Differential calculus applies to anything that changes or moves over time.