I am seeking to solve a set of nonlinear equations analytically. One of them is
1-x/y = f(z) exp(x)
Can I get further by applying derivative d/dx to both sides, which gives explicit expression for x for further use with the other equations.
x = ln(-1/(y*f(z))
Or is it nonsense to do that?
You loose Information if you derive an equation on both sides. All constants are annihilated which have essential necessity if you want to solve equations by one variable; it is not possible to use derivatives when solving equations. Therefore you must solve this equation numerically (such equations cannot be solved analytically in general), e.g. by fixed Point Iteration. You have:
$x = ln(\frac{1-\frac{x}{y}}{f(z)})$.
Then you can insert this equation on the right Hand side for x again and again.
Maybe, this wiki article can be useful.
Numerical method