Symbolic math toolbox- Jacobian of a function with respect to an other function?

I would like to find the jacobian of:

 f=[f(x1(t)...x6(t)); ... ;f6(x1(t)...x6(t))]

with respect to:

   x(t)=[x1(t);...;x6(t)]

which function could I use?

Is it possible to differenciate a symbolic function with respect to an other symbolic function?

Answer 1

[Walter Roberson]

No, it is not possible to differentiate with respect to a function. In a previous post several months ago I showed how that leads to a contradiction.

[Maria Perdomo]

Thanks!!

I think I found it:

http://www.mathworks.com/matlabcentral/answers/40904-how-to-symbolically-differentiate-a-function-with-respect-to-a-different-function

I got it, unlike variables, functions are not assumed to be independent and that can lead to contradictions.

[Frederik Rentzsch]

It seems to be possible since Release of R2021b.

syms x1(t) x2(t) 
syms f1(x1,x2) f2(x1,x2)
f = [f1 f2];
jacobian(f,[x1 x2])

works as intended but after f1 and f2 are defined x1 and x2 are no symfun-objects anymore. Bug?

[Sohini Sarkar]

Also see Functional Derivative: Functional derivative (variational derivative) - MATLAB functionalDerivative (mathworks.com)

Answer 2

[Alan Weiss]

 doc jacobian

Alan Weiss

MATLAB mathematical toolbox documentation