## Second order partial differential of implicite function

Posted December 3rd, 2009 by Structure

Let an equation defined by a function

Suppose we can apply the implicit function theorem in a neighborhood of a given point (a,b,c).

So we suppose

and

Then there is a function z=f(x,y) with f(a,b)=c; G(x,y,f(x,y))=0 or

We have

It is easy to see that