Function calls functions

Hello,

I have one question regarding a function definition. Can I retrieve a 
list of all functions which are called by a specified function including 
their function calls? I'll give an example for better understanding.

Imagine that I have created a set of functions in package cl-user over a 
long period of time. Now I'm not sure if I need all my functions. I'm 
sure that I need to call directly my function 'fun1' only. I would like 
to trace (list), which 'cl-user' functions calls the function 'fun1', so 
that I can delete unneeded functions. The call would be:

(give-me-all-functions-called-by 'fun1 :from-package 'cl-user)

result would be:

('fun2 'fun3 'fun5)

Thanks,
Lukas