An algebraic function is a function that can be written using a finite number of the basic operations of arithmetic (i.e., addition, multiplication, and exponentiation). In order to take the derivative of these functions, we will need the power rule.
The Power Rule: The power rule states that if , then .
Exponential Functions: An exponential function with base is its own derivative. That is to say, if , then as well.
Logarithmic Function: Logarithmic functions with base have derivatives of the following form: if , then .
What is the slope of when ?
To find the slope, we find the derivative of . But that is simply by the above rule. So the slope when is .
If , what is ?
Since we can take the derivative of each term separately,