Quotient rule

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

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


 * 1) Use the graph: This problem provides the graph or other representation of some functions. The student is expected to use the given information to find the value of the derivative at the particular point.Quotrule1.png
 * 2) Find directly: This problem provides a quotient of two functions and a particular point. The student is expected to find the derivative of the function at the particular point.Quotrule2.png

Strategies
Knowledge of the quotient 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))'=(g(x)f'(x)-f(x)*g'(x))/(g^2(x)).
 * 2) Because of non-commutativity of subtraction, the order of the derivatives does matter on the quotient rule.
 * 3) A mnemonic is "Bottom times the derivative of the top, minus the top times the derivative of the bottom."
 * 4) Another popular mnemonic is "LoDHi minus HiDLo all over LoLo."

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.