We shall know well about Schwarz Lemma, which states that:
Analytic function such that , then
, and .
We follow the scheme from the last post of Cartan Theorem, then we can get the estimate the derivative of .
Use the nested notation , and if we want to estimate , we shall write as:
, where .
for all .
However, this is just a thread for the estimation, we can easily see that , as we put .
The example is: . So, we can conclude that .
And for the derivative .