How to differentiate with respect to a symbolic function (which is a function of time)

syms t x

Fi = sym('Fi(t)') % time dependent symbolic variable

y = sin(Fi)*x % equation

symvar(y) % gives that y is dependent on x and t but not Fi

diff(y, Fi) % gives mupad error, obviously because according to matlab Fi is not a parameter of y

Given the example above, I have a function y, which is dependent on Fi and x. I can differentiate with respect to x and t, and it gives the right results but I cannot with respect to Fi.

So my question is: if I have a function y(Fi(t)), then how can I make matlab differentiate with respect to Fi?

Thanks in advance, Tamas

Answer 1

[Walter Roberson]

If Fi is known, then you do a change of variable if possible.

If Fi is not known, then you cannot do it.

See http://www.mathworks.com/matlabcentral/answers/40904-how-to-symbolically-differentiate-a-function-with-respect-to-a-different-function#comment_84171

[Tamas]

So the only workaround is to substitute Fi with an other variable and differentiate with respect to that?

I would assume that there must be an easy way to do this because in engineering it is usual that you have a variable changing in time, for example a position or speed coordinate...