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Ideally you should be able to do something like

Dh=h(x).diff(x).operator()
dg.substitute_function(Dh,f)

but unfortunately that doesn't work. I think it's a bug that it doesn't. Perhaps it can be fixed in the future.

A workaround is to define your function h so that it knows what its derivative is. For instance, you could just define h to be an antiderivative:

hprime=function('hprime')
h=hprime(x).integrate(x).function(x)

Then you can just execute your original code:

g=h(f(x,a,b));
dg=diff(g,x);

and then dg will be:

(a + b)*x^(a + b - 1)*hprime(x^(a + b))

Alternatively, you could define g as a symbolic function that knows what its derivative is called. This is a little technical and poorly documented, because it's probably intended for internal use:

hprime=function('hprime')
h=function('h',tderivative_func=lambda self,x,diff_param: hprime(x))

This produces the same result for dg, while preserving a concise form for g.

Ideally you should be able to do something like

Dh=h(x).diff(x).operator()
dg.substitute_function(Dh,f)

but unfortunately that doesn't work. I think it's a bug that it doesn't. Perhaps it can be fixed in the future.

A workaround is to define your function h so that it knows what its derivative is. For instance, you could just define h to be an antiderivative:

hprime=function('hprime')
h=hprime(x).integrate(x).function(x)

Then you can just execute your original code:

g=h(f(x,a,b));
dg=diff(g,x);

and then dg will be:

(a + b)*x^(a + b - 1)*hprime(x^(a + b))

Alternatively, you could define g as a symbolic function that knows what its derivative is called. This is a little technical and poorly documented, because it's probably intended for internal use:

hprime=function('hprime')
h=function('h',tderivative_func=lambda self,x,diff_param: hprime(x))
h=function('h',derivative_func=lambda self,*args,**kwargs: hprime(*args))

This produces the same result for dg, while preserving a concise form for g.