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Differentiation - The Product Rule

You may know hoe todifferentiate a simple function such asorGenerallyfunctions are built out of these simple functions to make morecomplicated functions and we must learn to differentiate these morecomplicated functions too. The simplest way two functions can becombined to make a more complicated function is to multiply them.Then they can be differentiated using the product rule:

The ProductRule:

If a function h consists oftwo simpler functionsandmultipliedtogether, then

Example: Differentiate

It is a good habit to getinto to write downandthen you can just substitute them into the expression for

Example: Differentiate

The product rule can be used repeatedly with any number ofproducts.

If a function h consists ofthree simpler functionsandmultipliedtogether, then

Example: Differentiate

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