How can I differentiate a function w.r.t. a dependent variable symbolically?

Hello everyone. I have a problem regarding differentiating a functions w.r.t. a dependent variable (let's say another function) - moreover this is a multivariate problem. I did solve it by hand actually, but the final version became so complicated that I wanted to verify the solution with Matlab, if I can.

The functions, just a part of them at least for instance are:

N=sin(t)+sin(t)*u;

x=3*cosh(t)+sin(u);
y=sinh(2*t)-9*sin(u);

I need to find:

diff(N,x,3);
diff(N,y,3);

and they should be in terms of t and u.

Any solution anyone would like to recommend?

PS: The functions are far too complicated than given here involving many sin, cos, sinh, cosh terms in fact. I just reduced them for the sake of context.

Answer 1

[Birdman]

According to the definition of diff function, the thing you want is not possible. See the attached figure.

[kandaz]

Yes, that is the error message I'm getting. I was just wondering whether there is any workaround, by defining functions in other ways, substituting variables, using inverse functions and their derivatives, etc?