The function is differentiable almost everywhere (this is a technical term from measure theory). Here's a pretty good explanation of its properties: https://epi

The function is differentiable almost everywhere (this is a technical term from measure theory). Here's a pretty good explanation of its properties: https://epicmath.org/2012/11/27/5-the-cantor-set-and-the-cantor-function/ https://epicmath.org/2012/11/27/5-the-cantor-set-and-the-can.... > The Cantor function, also known as the Cantor Staircase, is a bizarre function that is continuous and has a derivative of 0 at every point where it is differentiable. In fact, it is differentiable at every point other than on the Cantor set, which is a set of measure zero. So from a measure theoretic perspective the derivative of the Cantor function is well defined and it is equal to 0 almost everywhere. Almost everywhere equality is an equivalence relation and the derivative of the Cantor function is in the same equivalence class as the 0 function.