Basic Differentiation RulesThe CONSTANT Rule:The derivative of a constant function is 0.

Basic Differentiation RulesThe POWER Rule:

In the case of n = 1, the power rule is best thought of as a separate differentiation rule.

[ ] 1dx

dx

Basic Differentiation RulesThe POWER Rule:

Example:5 4

3 43 4

( ) '( ) 5

1 3( ) '( ) 3

f x x f x x

g x x g x xx x

Basic Differentiation RulesThe Constant Multiple Rule:

Example:5

5 5 4 4

3

[3 ] 3 [ ] 3(5) 15

y x

dy d dx x x x

dx dx dx

Basic Differentiation RulesThe Sum and Difference Rule:

Example:

Basic Differentiation RulesThe derivative of Sine and Cosine:

Example:

Rates of ChangeA function s that gives the position of an object as a function

of time t is called a position function.

Knowing that ,

the Average Velocity is

distancerate

time

Change in distance

Change in time

s

t

Rates of Change - Example

Rates of ChangeWhat if we wanted to know the velocity at a specific time

instead of the average velocity over an extended amount of time?

The instantaneous velocity is the derivative of the position function.

Note: Velocity can be negative, zero or positive.The speed is the absolute value of its velocity.

Rates of Change - Example