Over the weekend I was attempting to estimate the tension change in a bicycle spoke due to an applied load. After various simplifications and approximations, the problem was reduced to the following.
Given a constraint, F(x,y) = 0, and functions G(x,y) and H(x,y), find dG/dH at a particular point, here (0,0).
The constraint, F, was sufficiently complicated that solving for either variable was not feasible, so implicit differentiation seemed the best...