XPost: sci.math   
   From: user@example.net   
      
   Am 20.09.2014 um 21:20 schrieb IV:   
   > "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.   
   >   
   >   
      
   Once again, and the other answers to your post show that I am right. You have   
   your own  notation and terminology, which   
   is different from those used in standard mathematics. One has to guess what   
   you mean and then in answer posts you reveal   
   in a piecemeal way some clarifications. If you are not able to write down your   
   questions and/or ideas in way that others   
   can understand them, you will get no useful answers.Nix für ungut!, but   
   that's the truth.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)