A composed function is a function consisting of two or more functions that are connected in series.
The derivative of a composed function can be found with
Differentiation rule 4 (chain rule):
If then .
You can use this rule to prove the power rule for root functions:
If then for positive integer and .
Differentiation rule 5 (general power rule):
If then for any real value of .
To be able to prove the differentiation rule, you first need to learn how to differentiate exponential functions and logaritmic functions. That will come later.