So I'm having a bit of an issue in trying to take the derivative of an implicit function. The problem I'm trying to solve is this:
f(t,y(t)) = y' = e^(t-y)
Where the original function y(t) is some function of t, so I can't just treat y as a constant. I have to find the first four derivatives of this function, but I'm a bit confused on how to do this in Mathematica. I've looked at the documentation and it's not making much sense to me.
I did the first derivative by hand, and it becomes rather apparent that it's going to be tedious. Which is:
f'(t,y(t)) = (e^(t-y))(1-e^(t-y))