Course:MATH103/Archive/2010-2011/207/Notes/ExpAndLog

Exponential Functions and Their Derivatives

$e^{x}$

Differentiation Rules

$f(x)=e^{x}$

${\frac {dy}{dx}}\ e^{x}=e^{x}$

a^x

Differentiation Rules

f(x)= a^x

^d/_dx = a^xln(a)

Logarithmic Function and Their Derivatives

log_ax

^d/_dx = ¹/_{x ln(a)}

ln(x)

f(x) = e<sup>x

d</sup>/_dx(ln(x)) = ¹/_x

Review links

http://tutorial.math.lamar.edu/Classes/CalcI/LogFcns.aspx

http://tutorial.math.lamar.edu/Classes/CalcI/DiffExpLogFcns.aspx

http://www.themathpage.com/acalc/exponential.htm

you tube links

http://www.youtube.com/watch?v=5lfGha43hCU&feature=related

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/1/2imxMZskhHg

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/2/fmKqJ69YaTk

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/3/OvkZCZIGbQM

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/4/iYBDislrFYo

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/5/nI_AVqyIROs

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/6/ZGRu55zOOGU

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/7/nKsLl3TItKw

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/8/AIJ1vhQFsDc

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/9/BAkfNspJDNs

http://www.youtube.com/user/derekowens#p/c/ACE0A96797A74FB4/10/cj2qdPwUe9o

Excellent work so far.  A couple of ideas to expand on what you already have:
* Explore the connection between $e^{x}$ and $\ln(x)$
* Properties of the exponential and logarithm (e.g. $e^{a+b}=e^{a}e^{b}$, $\log(ab)=?$)
* Some examples that involve computing derivatives with the exponential and logarithm functions.
Also, I noticed that formulas might be a little time consuming the way you've been writing them out.  Here is a link that 
shows how to format math in the wiki http://meta.wikimedia.org/wiki/Help:Displaying_a_formula.  
Also, I suggest reading through the code for some of the lectures.  They contain plenty of examples of how to format math.
Feel free to copy and paste from these sources until you are comfortable with formatting math on your own.
CameronChristou