Calculus Portal
Objective 1b: The Quotient Rule
You will be able to derive and use the Product and Quotient Rules
Proof of the Quotient Rule
The derivative of a product of functions was not the product of the functions, so what makes you think a quotient would be any different. Well, it's plenty different, as you will see in this proof of the Quotient Rule. Duration: 11:30
Applying the Quotient Rule
Let's apply the Quotient Rule to a rational function here in Example 8, the first of two, of course. Duration: 3:48
Complex Fractions
In our second Example 8, we'll find the equation of a tangent line using the Quotient Rule on a function containing a complex fraction. Duration: 7:27
Avoiding the Quotient Rule
On Example 9, a rainbow reveals the secret to avoiding the Quotient Rule in 4 out of 5 cases. Duration: 6:01
Writing an Equation of a Tangent Line
Here we see the Quotient Rule applied to a function containing an exponential function, and then find the equation of a tangent line. Maybe you can guess the slope before we even start. Duration: 4:16
Algebra Before Calculus
Sometimes you have to do a bit of algebra before and after applying the Quotient Rule. And by sometimes, I mean all the time. Duration: 4:58
Product and Quotient Rules with Graphs
The AP Calculus Exam will present functions as an explicitly stated equations, a set of graphs, or a table of values. In Example 12, we see how to apply the Product and Quotient Rules to two graphed functions. Duration: 8:17
Product and Quotient Rules with Tables
Example 13 shows how to apply the Product and Quotient Rules to functions defined by a table of values. Stay tuned for a secret bonus problem. It will be totally worth your time. Duration: 10:13