Logarithms and Exponents
e
If 
Then by taking the natural log of both sides of the equations we get 
So 
are inverse functions of each other. This means is the reflection of y = 
over the line y = x.
e is unique in that the derivative of 
is and thus the integral of is also .
Proof:
For 
The format for finding a derivative
Factor out an
Substitute in 
The exponents of h cancel
The 1s inside the parentheses cancel
The h in the numerator and denominator cancel leaving the final answer
More generally we can say
(where u is an unknown function)
For example, find the following derivatives:
4.1 If 
4.2 
4.3 
Integrals of work the opposite of derivatives
Find the following integrals
4.4 
4.5 
4.6 
4.7 
4.8 
4.9 
4.10 
4.11 
