From: //noreply@axelvogt.de   
      
   On 19.07.2016 00:50, Richard Fateman wrote:   
   > On 7/18/2016 11:24 AM, Axel Vogt wrote:   
   >> Maple's notation (D(f) = derivative of f):   
   >>   
   >> int(x*D(f)(x^2),x);   
   >>                                      2   
   >>                               1/2 f(x )   
   >   
   > Maybe you need a better notation. What if f is   
   > a function of more than one variable?   
   >   
   > Conventional mathematics does   
   > not really provide a standard notation for   
   > "derivative of f with respect to its second formal argument"   
   > but a CAS need this, sometimes.  e.g. what is   
   > diff(f(g(x),h(x^2)), x) ?   
   >   
   > Mathematica makes up a notation like   
   >   
   >         2   (0,1)          2   
   > 2 x h'[x ] f      [g[x],h[x ]] + ...   
   >   
   > Maxima seems to require you to name these gradients, e.g. you could do   
   >   
   > gradef(f(u,v), f01(u,v), f10(u,v));   
   >   
   > how about Axiom, Fricas, Maple, DrHuang, etc?   
   > And anyone have a reputable reference to provide   
   > a mathematical standard?   
      
   The notation assumes f to be univariate, else one has to   
   provide the 'number' of the variable like   
      
   int(x*D[1](f)(x^2,y),x); # = w.r.t. the first variable   
      
                                        2   
                                 1/2 f(x , y)   
      
   For diff(f(g(x),h(x^2)), x) the output is using the chain   
   rule and displays D[1](f)( g(x),h(x^2) )*diff(g(x),x) +   
   2*D[2](f)( g(x),h(x^2) )*D(h)(x^2)*x , or on demand:   
      
   D[1](f)(g(x),h(x^2))*D(g)(x)+2*D[2](f)(g(x),h(x^2))*D(h)(x^2)*x   
      
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