# Substitute a function in a formal derivative

This gives a nice result.

```
var('p w0 c g dc dg dp dw0')
EUa=function('EUa')(p,w0,c,g)
EUa_c=diff(EUa,c)
EUa_g=diff(EUa,g)
#
EUna=function('EUna')(p,w0,c,g)
EUna_g=diff(EUna,g)
EUna_c=diff(EUna,c)
##
dEUa=EUa_c*dc + EUa_g*dg
dEUna=EUna_c*dc + EUna_g*dg
###
show(EUa)
show(EUna)
show(dEUa)
show(dEUna)
sol=solve(dEUa==dEUna, dg)
sol=(sol[0]/dc).full_simplify()
show(sol)
```

But now, I would like to substitute to `EUa(p,w0,c,g) = p*U(w0)+(1-p)*U(0)`

and `EUna(p,w0,c,g) = p*U(w0-c)+(1-p)*U(g*w0-c)`

then, later change the unknown function `U(w)`

to say `ln(w)`

or `w^(1/2)`

. I suppose I need to define first a function `U=function('U')(w)`

after to define `w`

as a variable. But all my tentatives fail.

Hints :

use variable names in formal differentiations (e. g.

`diff(f(x,y).x)`

instead of`diff(f, x)`

).lookup

`substitute_function?`

Hi @Emmanuel Charpentier

SageMath 9.2 notebook , W10

Object

`substitute_function`

not found.It's a method of symbolic expression objects. Dotting the "i"s and crossing the "t"s, try :

[ Snip...]