The chain rule allows us to take the derivatives of composite functions, such as the function
 
 

(see answer below), with relative ease--once you get used to the how the rule is applied.
 

We start with the composite function
 
 

and take the formal derivative of 
 
 

and then replace with the composite function to obtain
 
 
 

Now, we apply a trick to help us resolve the limit (similar to what we did in the product rule derivation) to rewrite the derivative of as
 
 
 

To make it easier to see how to resolve this limit we let andand note that as we also have that . So the derivative of  above can be rewritten as
 
 
 

which gives us the result
 
 

This is written more properly by replacing above with   to obtaiin the final result
 
 
 

We can now apply the chain rule to the function
 
 

First we rewrite the function as
 
 

Then, we apply the chain rule to the above composite function to obtain the derivative