Chain Rule: Quantity 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 8th 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:
We can use the
Sum, Scalar Multiple, and Power Rules to complete the problem by differentiating the remaining terms to get 
Test Problem: Find the derivative of 
