Product rule
With the product rule you can calculate the derivative of a product of two functions
Explanation
This rule can be explained in an elegant way by calculation with infinitely small transitions
The product gives here
what you can write as
The increase consist of three terms
Substitution in the definition of the derivative gives
The limit of a sum is the sum of the limits, so
where the third term is neglectable. Therefor we get
so
You can guess what the product of 3 functions will look like.