3.8 Derivatives of Logarithmic Functions

Hey class. Hope all of you enjoyed homecoming. Sorry that the game wasn't much of a show. Poly next week though so keep up the spirits. Well its time for math again, and this concept can be pretty difficult.

There are two basic equations in this section that the others are derived from:
For the first equation it is 1 over both x and ln of the base a

and the second equation is simply one over x when taking the derivative of the natural log of a number

From the second equation, if the the "x" is a polynomial or complex equation that we'll designate as "u" then it is 1 over the equation "u" multiplied by the derivative of that equation:

Logarithmic Differention is basically just applying logarithmic rules to simplify an equation so that its derivative can be taken easier.

Here is a simple example from the book of logarithmic differentiation:

Differentiate:

1. In the first step we took the natural log "ln" of both sides, and therefore the exponent came down.
2. In the next step using the product rule we took the derivative of that term. Specifically we took the first term times the derivative of lnx which is 1/x plus lnx times one over twice the square root of x.
   
3. In the third step we multiplied y to both sides in order to isolate y' on one side.

To express e as a limit:
As x approaches zero

As n approaches infinity


Additional Links
Another Review
A GREAT place to practice derivatives of logs with sample problems and solutions


MAGNUS you're up next.




This is Maurice Drew, he came out of UCLA last year so this is his rookie season. He's 5'7" and thats football height so he's probably shorter and 200 pounds. His legs as you can see are ginormous and people often mistake him for having pads on when he does not. This season he has 187 yds. and 3 touchdowns.


This is Mr. C who taught geometry here last year as well as coached the 400 team. He is really fast. He holds the prep league record in the 400 and the 200. Mr. C ran track in college at Amherst. He is currently in med school at USC.