From: ivgroups@onlinehome.de   
      
   "IV"  wrote in news:lvjrcs$shh$1@online.de...   
      
   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.   
      
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