Functional derivative : function_diff

### 2.17.1 Functional derivative : `function_diff`

`function_diff` takes a function as argument.
`function_diff` returns the derivative function of this function.
Input :

`function_diff(sin)`

Output :

`(‘ x‘)->cos(‘ x‘)`

Input :

`function_diff(sin)(x)`

Output :

`cos(x)`

Input :

`f(x):=x```^```2+x*cos(x)`
`function_diff(f)`

Output :

`(‘ x‘)->2*‘ x‘+cos(‘ x‘)+‘ x‘*(-(sin(‘ x‘)))`

Input :

`function_diff(f)(x)`

Output :

`cos(x)+x*(-(sin(x)))+2*x`

To define the function g as f′, input :

`g:=function_diff(f)`

The `function_diff` instruction has the same effect as using the expression derivative in conjonction with `unapply` :

`g:=unapply(diff(f(x),x),x)`
`g(x)`

Output :

`cos(x)+x*(-(sin(x)))+2*x`

Warning !!!
In `Maple` mode, for compatibility, `D` may be used in place of `function_diff`. For this reason, it is impossible to assign a variable named `D` in `Maple` mode (hence you can not name a geometric object `D`).