Three questions on Maxima



Dear colleagues,
I am novice in using Maxima CAS, so I have numerous questions. Here are three of these. May be, you'll be so kind to answer me.
1. What is the way to obtain the list of digits of an integer? In Mathematica, I simply write IntegerDigits[number].
2. What is a way to define a function that will memorise its values? 
3. How can I get the value of the derivative of a given function? In Mathematica, I can use f'[x] instead of D[f[x],x].
Sincerely yours,
Oleg Ivanov,
St.Petersburg State University