The diff command counts faster than ∂/∂x

[Albert Chan]

Differentiation, unlike integration, is very mechanical, and should run very fast.
Problem is internal hard-coded simplify, that cannot be controlled by SIMPLIFY setting.

My guess is diff(f,x) is less "simplified" than ∂(f,x), thus run much faster.

OP problem, we want to stop sum from simplify f with common denominator, making a mess.
Instead of summing an expression, we sum a list, which bypass internal simpilfy code. (*)

Cas> lst := makelist(k -> (-1)^(k+1)/k^x, 1, 20)
Cas> f := sum(lst)

diff(f,x) or ∂(f,x) should now run very fast.

(*) sum(lst) = '+' operator applied to list, see https://www.hpmuseum.org/forum/thread-20...#pid176469

Cas> (a+b)[1] (lst)

1 - 1/2^x + 1/3^x - 1/4^x + 1/5^x ... + 1/19^x - 1/20^x