Differentiation RulesThe PRODUCT Rule:

In other words, if y = fg then y’ = fg’ + f’g

If y = fgh then y’ = f’gh + fg’h + fgh’

Example

Example

Differentiation RulesThe QUOTIENT Rule:

In other words, if , then f

yg

2

' ''gf fg

yg

Example

Example

Differentiation Rules The TRIGONOMIC Functions:

These can all be derived from the quotient rule and the derivatives of sine and cosine.

You should become familiar with these!

ExampleThe TRIGONOMIC Functions:

ExampleThe TRIGONOMIC Functions:

NOTE: Because of trigonometric identities, the derivative of a trigonometric function can take many forms.

High Order DerivativesJust as a velocity function can be obtained by deriving a

position function, acceleration can be obtained by deriving a velocity function. Another way of saying this is that the acceleration function can be obtained by deriving the position function twice.

High Order Derivatives

Example