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Differentiate symbolic composite function

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Carmelo
Carmelo 2014-6-3
评论： Carmelo 2014-6-6
Hello,
I am currently using MATLAB R2013a and I am trying to differentiate an expression in order to obtain a symbolic non linear differential equation. The expression has the following form:
syms t a(t) b(t) c(t)
f=f(a(t),b(t),c(t))
where neither a(t), b(t) nor c(t) are known in their functional form, but the relation f(a(t),b(t),c(t)) is known in it's functional form. I wish to obtain:
df/da=g(a(t),b(t),c(t))
df/db=h(a(t),b(t),c(t))
df/dc=k(a(t),b(t),c(t))
I define the composite function f(a(t),b(t),c(t)), MATLAB recongnizes only a function of t f=f(t). I perform the following symbolic operations:
diff(f,a(t))
diff(f,b(t))
diff(f,c(t))
MATLAB does not recognize f as a composite function of a(t), b(t), c(t) and cannot perform the above differentiations. I cannot remove the time dependence a(t), b(t), c(t) since it will then be necessary to derive with respect to time.
Is some solution known for a problem of this type?
Thank you in advance.
Carmelo.

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采纳的回答

Deepak Ramaswamy
Deepak Ramaswamy 2014-6-4
Does this work?
syms t at bt ct
f = at*bt*ct*t;
syms a(t) b(t) c(t)
dfda = subs(diff(f,at),[at,bt,ct],[a(t),b(t),c(t)])
dfa =
t*b(t)*c(t)
I probably missed why time dependence can't be removed
  1 个评论
Carmelo
Carmelo 2014-6-6
Thank you, I guess the subs function is the key. Time dependence couldn't be removed since I need to later solve the differential equation.
Best regards.

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