On 01/15/2013 05:06 AM, Levi Wiseman wrote:
> Is there a way to conduce Maxima to solve an application of the chain
> rule to the composition of an abstract function and a concrete
> function? E.g. I'd like 'g(x):=x^2$ diff(f(g(x)),x);' to produce
> '(df/dg)(2x)'. Right now it only produces 'd(f(x^2))/dx'.
>
> Using 'g(x):=x^2$ depends(f,g,g,x)$ diff(f,x);' kind of works. I get
> '(df/dg)(dg/dx)', but I'd like 'dg/dx' to be solved.
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you can use "gradef" to define a new function that's the abstract
derivative of f with respect to its argument.
(%i2) g(x) := x^2;
(%o2) g(x):=x^2
(%i3) diff(f(g(x)),x);
(%o3) 'diff(f(x^2),x,1)
(%i4) gradef(f(z),fpm(z));
(%o4) f(z)
(%i5) diff(f(g(x)),x);
(%o5) 2*x*fpm(x^2)