I wanted to know if Matlab is able to take the argument diff(y,x) given that x and y are functions of t, and derive and then output the equation diff(y,t)/diff(x,t) on its own. Can Matlab do that?
NO
MATLAB cannot take derivatives with respect to a function. Normal calculus cannot take derivative with respect to a function; you need Calculus of Variations for that.
It is often suggested to substitute a variable for the function, take the derivative with respect to the variable, and then substitute back the function for the variable in the result. However, in order for that to work, the two parts have to be independent, and that is something that you cannot guarantee when you do not know what the functions are.
The closest you can get is to take the hypothesis that the functions are independent, and do the substitution, derivative, substitution route, figure out what the function is, and then go back and test to see whether the derivative holds true.
At some point I posted a specific example of where the technique failed, but unfortunately I have long lost track of that example.
syms X
subs(diff(subs(f, x, X),X),X,x) %change function to symbol, take derivative, subs back
Reminder: this can give incorrect answers if the parts are not truly independent.
