We start by letting  for which we want to find the derivative .

We have already derived the relationship
 
 

Now, we note that  and so we may continue the above line as
 
 
 

We evaluate , where y =  by looking at the right triangle in which the relationship
 
 

holds. So, in this triangle the side opposite the angle  equals , the hypotenuse equals , and the side adjacent to the angle  equals 1.

This is a triangle as below
 
 
 

Therefore, we have that the derivative of  is given by
 
 

or,