Oh, I'm sorry, I wasn't aware of those possibilities.
So once again. Here is a sample code :
ClearAll[Eta, CapitalPhi, Phi, Delta, OrderDev, x, z, t, i, n, K, dxphi, dzphi, dxphis, dzphis];
OrderDev = 1;
i = 0;
Eta[x_, t_] := Sum [K[n][t] x^(2 n)/(2 n)!, {n, 0, OrderDev}];
Delta[ z_, t_] := z - K[0][t];
CapitalPhi[x_, z_, t_] := -Sum [Phi[n][t] Cos[n x - i Pi] Exp[-n Delta[z, t]], {n, 1, OrderDev}];
dxphi[x_, z_, t_] := D[CapitalPhi[x, z, t], x];
dzphi[x_, z_, t_] := D[CapitalPhi[x, z, t], z];
dxphis[x_, t_] := dxphi[x, Eta[x, t], t];
dzphis[x_, t_] := dzphi[x, Eta[x, t], t];
Mathematica doesn't understand what I say, which shows that I'm saying it wrong. When I ask
dxphi[x, z, t]
It answers
E^(-z + K[0][t]) Sin[x] Phi[1][t]
Which is OK with me, but then,
dxphis[x, t]
Produces
E^(-(1/2) x^2 K[1][t]) Sin[x] Phi[1][t] + E^(-(1/2) x^2 K[1][t]) x Cos[x] K[1][t] Phi[1][t]
When I expect
E^(-(1/2) x^2 K[1][t]) Sin[x] Phi[1][t]
Worse, in the case of
dzphis[x, t]
It says
General::ivar: K[0][t]+1/2 x^2 K[1][t] is not a valid variable. >>
So I assume that when I say something like
$g(x)= {\partial f \over \partial x}$ and then
$h(x) = g(u(x))$, it keeps the memory of the definition of
$g$ and gives
${\partial f \over \partial x} (u(x)) \times u'(x)$, while I was looking for
${\partial f \over \partial x}| _ {\ u(x)}$.
Could you help me to define dxphis and dzphis in a proper way ?
Thank you in advance for your attention.
