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Let's dissect this case :

sage: f=function("f")
sage: g=function("g")

Sage knows the chain rule, but expresses it in a somewhat unusual form :

sage: diff(g(f(x)),x)
diff(f(x), x)*D[0](g)(f(x))

Let's try to understand it :

sage: diff(g(f(x)),x).operands()[1]
D[0](g)(f(x))
sage: diff(g(f(x)),x).operands()[1].operator()
D[0](g)

This is not a "usual" function, but it has arguments :

sage: diff(g(f(x)),x).operands()[1].arguments()
(x,)

and is applied to a list of arguments :

sage: diff(g(f(x)),x).operands()[1].operands()
[f(x)]

When applied to x, it returns the valye od the derivative of f at the point x :

sage: diff(g(f(x)),x).operands()[1].operator()(x)
diff(g(x), x)

but it applies to any value, including an unrelated variable :

sage: var("t")
t
sage: diff(g(f(x)),x).operands()[1].operator()(t)
diff(g(t), t)

This object is not a symbolic expression :

sage: diff(g(f(x)),x).operands()[1].operator() in SR
False

so let's investigate :

sage: type(diff(g(f(x)),x).operands()[1].operator())
<class 'sage.symbolic.operators.FDerivativeOperator'>

You should read help(type(diff(g(f(x)),x).operands()[1].operator()))... Note that FDerivativeOperator isn't directly accessible :

import_statements(type(diff(g(f(x)),x).operands()[1].operator()))
from sage.symbolic.operators import FDerivativeOperator

And that the ? interface to its help fails :

sage: FDerivativeOperator?
[ in the *Messages* buffer of emacs : ] Object FDerivativeOperator not found.

HTH,

Let's dissect this case :

sage: f=function("f")
sage: g=function("g")

Sage knows the chain rule, but expresses it in a somewhat unusual form :

sage: diff(g(f(x)),x)
diff(f(x), x)*D[0](g)(f(x))

Let's try to understand it :

sage: diff(g(f(x)),x).operands()[1]
D[0](g)(f(x))
sage: diff(g(f(x)),x).operands()[1].operator()
D[0](g)

This is not a "usual" function, but it has arguments :

sage: diff(g(f(x)),x).operands()[1].arguments()
(x,)

and is applied to a list of arguments :

sage: diff(g(f(x)),x).operands()[1].operands()
[f(x)]

When applied to x, it returns the valye od the derivative of f at the point x :

sage: diff(g(f(x)),x).operands()[1].operator()(x)
diff(g(x), x)

but it applies to any value, including an unrelated variable :

sage: var("t")
t
sage: diff(g(f(x)),x).operands()[1].operator()(t)
diff(g(t), t)

This object is not a symbolic expression :

sage: diff(g(f(x)),x).operands()[1].operator() in SR
False

so let's investigate :

sage: type(diff(g(f(x)),x).operands()[1].operator())
<class 'sage.symbolic.operators.FDerivativeOperator'>

You should read help(type(diff(g(f(x)),x).operands()[1].operator()))... Note that FDerivativeOperator isn't directly accessible :

import_statements(type(diff(g(f(x)),x).operands()[1].operator()))
from sage.symbolic.operators import FDerivativeOperator

And that the ? interface to its help fails :

sage: FDerivativeOperator?
[ in 

[in the *Messages* buffer of emacs : ] ] Object FDerivativeOperator not found. found.

HTH,

Let's dissect this case :

sage: f=function("f")
sage: g=function("g")

Sage knows the chain rule, but expresses it in a somewhat unusual form :

sage: diff(g(f(x)),x)
diff(f(x), x)*D[0](g)(f(x))

Let's try to understand it :

sage: diff(g(f(x)),x).operands()[1]
D[0](g)(f(x))
sage: diff(g(f(x)),x).operands()[1].operator()
D[0](g)

This is not a "usual" function, but it has arguments :

sage: diff(g(f(x)),x).operands()[1].arguments()
(x,)

and is applied to a list of arguments :

sage: diff(g(f(x)),x).operands()[1].operands()
[f(x)]

When applied to x, it returns the valye od the derivative of f at the point x :

sage: diff(g(f(x)),x).operands()[1].operator()(x)
diff(g(x), x)

but it applies to any value, including an unrelated variable :

sage: var("t")
t
sage: diff(g(f(x)),x).operands()[1].operator()(t)
diff(g(t), t)

This object is not a symbolic expression :

sage: diff(g(f(x)),x).operands()[1].operator() in SR
False

so let's investigate :

sage: type(diff(g(f(x)),x).operands()[1].operator())
<class 'sage.symbolic.operators.FDerivativeOperator'>

You should read help(type(diff(g(f(x)),x).operands()[1].operator())) and the documentation of operators ... Note that FDerivativeOperator isn't directly accessible :

import_statements(type(diff(g(f(x)),x).operands()[1].operator()))
from sage.symbolic.operators import FDerivativeOperator

And that the ? interface to its help fails :

sage: FDerivativeOperator?

[in the *Messages* buffer of emacs : ] Object FDerivativeOperator not found.

HTH,