(NOT A HW QUESTION!) Saw this when browsing facebook groups View attachment 7253 It reminds me some diff eqt stuff learnt back in 2nd year e.g. [f^2]'=2(f'*f) e.g. f'=f f=0 or sum(exp(lx),x) From fractional calculus, I also briefly came across a function f such that f(f(g))=g' http://en.wikipedia.org/wiki/Fractional_calculus so what kind of function, when multiplied to the right of another function, will have the same effect as differentiating it? From a thread a year ago (answered by rpenner and soem other math guys), I have learnt some basic techniques in solving a function equation including substitutions, looking for patterns and trial and error But for this one I am at lost on how to solve it Trying to do a dirct integration by collapsing the f'f part into a product rule give me a nonlinear ODE (just as some other guy has done on the comments) of the form f^2-f'=c, so it does not really help