Consider a complex function y
with a real argument x
and the function y
itself is an argument of another function f
, which takes the 2nd-derivative of y
with respect to x
f[y_] := y''[x]
It seems that ComplexExpand
gives the right answer
ComplexExpand[f[yr + I*yi]]
(*((I yi + yr)^\[Prime]\[Prime])[x]*)
Well, when I try to extract its real and imaginary parts separately, the following approaches failed.
ComplexExpand[Re@f[yr + I*yi]]
(*((I yi + yr)^\[Prime]\[Prime])[x]*)
Re@ComplexExpand[f[yr + I*yi]]
(*Re[((I yi + yr)^\[Prime]\[Prime])[x]]*)
ComplexExpand[f[yr + I*yi]] // Re
(*Re[((I yi + yr)^\[Prime]\[Prime])[x]]*)
I expect to obtain something like yr''[x]
and yi''[x]
for the real and imaginary parts.
Can anyone help with this?
ComplexExpand
expression accomplishes nothing:f[yr + I*yi] == ComplexExpand[f[yr + I*yi]]
. $\endgroup$y
has a real argumentx
, and another functionf
takes derivative ofy
w.r.t.x
. Please see my update. $\endgroup$y[x]=yr[x]+i*yi[x]
w.r.t. $x \in R$ and gety'[x]=yr'[x]+i*yi'[x]
for example. $\endgroup$