Hi! I've got a question about implicit functions.(adsbygoogle = window.adsbygoogle || []).push({});

I have to solve a system f(x,y,z)=0 in the neighbourhood of (1,1,1). I have a problem computing the derivative of an implicit function (x,y)=g(z), whose existence is given by the implicit function theorem when applied to the given function f(x,y,z) which goes from R^3 to R^2. I use as it seems two equivalent standard methods.

I compute the Jacobi matrix of f and check whether the minor - a square matrix - is invertible at the given point. Then I invert it and with one more step get the derivative of g at z=1.

The other method is: I use implicit differentiation, i.e. I differentiate the system f(x,y,z)=0 directly and get differentials dg_1/dz, dg_2/dz (because g is two-component).

Now I get two different answers with either method. The difference is only the sign, but I cannot figure out WHY there is sign change! Is there anything I should pay attention to when I use these two methods? I mean they are basically the same! I checked each step in both of them. What could be the reason for the difference?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Implicit Function

**Physics Forums | Science Articles, Homework Help, Discussion**