Throughout this module, if something does not exist, write DNE in the
answer box.
Recap Video
Take a look at the following video which recaps the ideas from the section.
_
Example Video
Below are two videos showing worked examples.
Problems
Here are the derivative rules you should know from the section:
Let and be
differentiable functions. Then:
- (Product Rule) .
- (Quotient Rule) .
If , find .
Notice that is the product of two functions, let’s call them and
(so ) with
The product rule says
Notice by the power rule, and . Therefore,
If , evaluate .
This function is a quotient of two functions and . We can write
where
The quotient rule says
Notice
Plugging everything in, we get
Suppose with and . Then .
We can use the product rule to differentiate .
Doing so gives
Now plug in .
Consider . How many points are there on the graph of where the tangent
line is horizontal? .
Use the quotient rule to differentiate and simplify the
derivative.
The only way for a fraction to equal is if the numerator equals
.
List them in increasing order: