Differentiate symbolic composite function

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.

Answer 1

[Deepak Ramaswamy]

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

[Carmelo]

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.