This document discusses differentiation rules for finding derivatives of various types of functions including linear functions, constant functions, power functions, constant times a function, sums of functions, and differences of functions. It provides examples of finding the derivatives of f(x)=x, f(x)=5, f(x)=x^4, f(x)=2x^4, and functions that are sums and differences of multiple terms like g(x)=1/2x^5 - 2x^3 + 1/2x^2 - 7 and h(x)=x^3 + 2x-2 - x^1/2.

1. Differentiation Rules
The Definition of a Derivative
Mathematics is the science of pattern ... let's look for some patterns ...
Let's use the definition to find some derivatives ...

2. The Derivative of a Linear Function
Find the derivative of

3. The Derivative of a Constant Function
Find the derivative of

4. The Derivative of a Power Function
Find the derivative of f(x) = x4

5. The Derivative of a Constant Times a Function
Find the derivative of f(x) = 2x4

6. The Derivative of a Sum of Functions

7. The Derivative of a Difference of Functions

8. Find the derivative of
g(x) = 1 x5 - 2x3 + 1 x2 - 7
2 2
1
2
h(x) = x3 + 2x-2 - x