Substitute partial differential into symfun

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ludolfusexe
ludolfusexe 2024-5-15
评论： ludolfusexe 2024-5-16
Ran in:
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!

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采纳的回答

Torsten
Torsten 2024-5-15
移动：Torsten 2024-5-15
Ran in:
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 = 
  2 个评论
Paul
Paul 2024-5-15
编辑：Paul 2024-5-15
Ran in:
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
ludolfusexe 2024-5-16
Thank you very much for your two answers, both are very helpful.

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