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## 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).

giac documentation written by Renée De Graeve and Bernard Parisse