XPost: sci.math   
   From: ivgroups@onlinehome.de   
      
   "Pirx42"  wrote in news:lvjsiu$c6b$1@dont-email.me...   
   >> I am interested here in *symbolically* given functions, that means in   
   >> expressions of some Special functions (Named functions), e.g. the   
   >> Elementary functions. Let all be in the Real numbers or in the   
   >> Complex numbers. Let the domains of the functions unconsidered.   
   >> Working with the expression cos(arcsin(x)) = sqrt(1-x^2), I found the   
   >> following general problem:   
   >> Let us assume that the compositional inverse f_ = f_(x) of a given   
   >> function f = f(x) is or would be unknown. When (under what   
   >> circumstances) can a symbolically given expression df(x)/dx at x =   
   >> f_(x) be represented symbolically without the   
   >> unknown inverse function f_?   
   >> Thanks.   
      
   > Nix verstehen.   
   > You have to be more precise. What you say makes no sense to me.   
   > What is the "compositional inverse" of a function, simply the inverse   
   > function f^{-1}?   
   > If you have problems formulating, wikipedia is your friend; but I think,   
   > maybe you should just befriend a mathematician in your acquaintancies and   
   > get   
   > your   
   > formulations and terminology right.   
   > As you pose your questions, nobody here can answer them IMHO. Maybe I am   
   > wrong, we'll see.   
      
   Yes, the compositional inverse is the inverse of the composition. It is not   
   the multiplicative inverse. (If you have problems understanding, *Google* is   
   your friend. Nix für ungut!) Wikipedia has not all the technical terms which   
   I know from the specific scientific articles of the respective special   
   mathematical fields (e.g. Computer algebra, Generating functions,   
   Combinatorics).   
      
   I have an important application of the answers to this mathematical problem   
   in mathematics, and in some other non-mathematical usages - usages with   
   importance / with impact to the real life.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)