Chain Rule: Linear raised to a power
The
Chain Rule can be applied to find the derivative of a function such as
That is because this function can be considered (from the outside working in) as a quantity raised to the 3rd power. Frequently, it helps to temporarily define a variable, u, to represent the quantity.
Then 
. Here, 
Then the function can be written as
, and the task of finding its derivative with respect to x becomes
.
The first stage, finding 
can be handled with the
In order to go further, we need to replace u with its equivalent:
