Substitute partial differential into symfun

Because my actual functions are very complex, I would like to calculate the derivative of nested functions first and then substitute the functions afterwards.

A minimal example looks like this:

syms G(h) h(t) t 
Q    = G(h)

Q = 

dGdt = diff(Q,t)   % -> D(G)(h(t)) occurs

dGdt = 

% Now define G(h) and derive:
G    = h^2;
dGdh = diff(G,h)

dGdh(t) = 

How is it possible, to insert the derivative of G with respect to h as the partial derivative?

I tried this, but it is not working:

% dQ_subs = subs(dGdt, D(G), dGdh)
% dQ_subs = subs(dGdt, D(G)(h(t)), dGdh)

I really appreciate any feedback!

Answer 1

[Torsten]

syms G(h) h(t) t 
Q    = G(h)

Q = 

dGdt = diff(Q,t)   % -> D(G)(h(t)) occurs

dGdt = 

s = children(dGdt)

s = 1x2 cell array
    {[D(G)(h(t))]}    {[diff(h(t), t)]}

% Now define G(h) and derive:
G    = h^2;
dGdh = diff(G,h)

dGdh(t) = 

subs(dGdt,s{1},dGdh)

ans = 

[Paul]

Hi Torsten,

I think it works easier, and perhaps more generally, to define G as a function of its own dummy variable.

syms G(x) h(t) t
Q    = G(h);
dGdt = diff(Q,t)   % -> D(G)(h(t)) occurs

dGdt = 

% Now define G(x) and derive:
G(x)    = x^2;
subs(dGdt)

ans = 

Slightly more complicated case

G(x) = x^2 + sin(x);
subs(dGdt)

ans = 

[ludolfusexe]

Thank you very much for your two answers, both are very helpful.