You may know hoe to differentiate a simple function such as
or
Generally functions are built out of these simple functions to make more complicated functions and we must learn to differentiate these more complicated functions too. The simplest way two functions can be combined to make a more complicated function is to multiply them. Then they can be differentiated using the product rule:
The Product Rule:
If a function h consists of two simpler functions
and
multiplied together, then
Example: Differentiate
It is a good habit to get into to write down
and then you can just substitute them into the expression for
Example: Differentiate
The product rule can be used repeatedly with any number of products.
If a function h consists of three simpler functions
andmultiplied together, then
Example: Differentiate
