Combining the product and chain rules

The  exercise appears under the Differential calculus Math Mission. This exercise applies the chain rule in contexts where the product rule is also applied.

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


 * 1) Find directly: This problem provides a composition of two functions and a particular point. The student is expected to find the derivative of the function at the particular point.Ctpacr1.png
 * 2) Answer the conceptual question: This problem provides several potential functions and has a question that involves some application of the derivative rules. The student is expected to answer the question and provide the answer in the space provided.Ctpacr2.png

Strategies
Knowledge of all the differentiation rules, though particularly product and chain, are encouraged to ensure success on this exercise.
 * 1) The problems in this exercise bring together several of the other rules, which is more common in real-life applications.

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.