Question: solving 3 equations sequentially

Hello,

although I manage to solve the following problem step by step, I don't really know how translate it properly into Maple code.

First of all, from the following equation I have to extract the derivatives dx/dy1 and dx/dy2 (because I need them later on):

f(x,y1,y2)=0

(This can be done using the implicit function theorem).

Then, I have to calculate the following derivate and set it equal to zero to get y1 as a function of y2.

dg1(x,y1)/dy1 = 0

Combining the two results above should allow me to solve the following equation for y2.

dg2(x,y2) / dy2 = 0

Note that this derivative will require dx/dy2 which, in turn, will be a function of y1. It is important that the last two equations are not solved simultaneously, but in the given order, such that y1=y1(y2) can be inserted into the last equation. Furthermore, it would be good to have a solution that does not require solving the first equation for x(y1, y2) explicitly, because this might not be possible. Since this is only a simplified version of my problem which, in general, will probably only be solvable numerically, the solution might as well use the fsolve() command (in the end).

I would be very grateful for any comments, since I'm really struggling with this problem.

Thanks a lot,

ciccarese