Chapter 5-4

Differentiation of Exponential Functions

The following section describes how to find the derivative of an exponential function using the chain rule.

Equations:

Simple Derivative
d/d(x) (e^x) = (e^x)

verbally: the derivative of the function "e" to the "x" is equal to "e" to the "x."

Chain rule:
d/d(x) (e^f(x)) = (e^(f(x)))(f ' (x))

verbally: the derivative of "e" raised to some function f(x) is equal to "e" raised to some function f(x) multiplied by the derivative of f(x).


*Note: do not use the power rule on an exponential function, you can only perform the power rule when "x" is in the base of the function.

Example:
e^(2x+3)
Using the chain rule we find that e^(2x+3) = e^(2x+3) d/dx (2x+3) = e^(2x+3)(2) = 2e^(2x+3)

Other Sources for Differentiation of Exponential Functions:
http://www.tcc.edu/VML/Mth163/documents/DifferentiationofExponentialFunctions.ppt#3
http://www.analyzemath.com/calculus/Differentiation/exponential.html
http://www.lgfl.net/lgfl/leas/sutton/web/Resources/mathematics/Diff%20exp%20fns.xls
http://webpages.charter.net/mgroves9/explogdiff.html

Next for the Blog is Danica for Chapter 5-5 Differentiation of Logarithmic Functions

Personalization:
Top ln(e^10) reasons why e is better than pi.
10) e is easier to spell than pi.
9) pi ~= 3.14 while e ~=2.718281828459045.
8) The character for e can be found on a keyboard, but pi sure can't.
7) Everybody fights for their piece of the pie.
6) ln(pi^1) is a really long number, but ln(e^1) = 1.
5) e is used in calculus while pi is used in baby geometry.
4) 'e' is the most commonly picked vowel in Wheel of Fortune.
3) e stands for Euler's Number, pi doesn't stand for anything.
2) You don't need to know Greek to be able to use e.
1) You can't confuse e with a food product.