Let's say that I have some symbolic expression of a function $x(t)$, and would like to obtain its derivative $x'(t)$.

However, I also have the following two identities, $\xi = \omega t$, and $\eta = \epsilon t$.

Is there any way to have Mathematica symbolically express $x'(t)$ in terms of partials of $\xi$ and $\eta$?

I've already attempted the method recommended by Alex in a related question here, but it doesn't seem to work for this situation. Ideally, the method would preserve the structure of the equations so that one could use DSolve or other standard symbolic manipulations on them.

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You should look at DChange

DChange[D[X[t], {t, 1}], eta == w*t, t, eta, X[t]]

w X'[eta]

Note: For change of variable, there should be one to one correspondence. So, it seems impossible to change $t$ to $\eta$ and $\xi$ at the same time. Correct me if I am wrong.

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