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

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kandaz
kandaz 2018-3-29
评论： kandaz 2018-3-29
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.

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Birdman
Birdman 2018-3-29
编辑：Birdman 2018-3-29
According to the definition of diff function, the thing you want is not possible. See the attached figure.
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kandaz
kandaz 2018-3-29
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?

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