Let F: be a function for which F(x+y,y+z)=0 defines implicitly z=f(x,y) around a point (a,b,c). Verify that in (a,b)
I'm having difficulty with getting rid of some derivatives, they should cancel out I guess.
(It's a bit heavy to read but please take a look at my work)
First, I apply the chain rule with u=g(x,y)=x+y, v=h(x,y)
and get the expressions for dz/dx and dz/dy
dF/dx=dF/du dg/dx+dF/dv dh/dx=dF/du+dF/dv dz/dx
solve for dz/dx,
From dF/dz=dF/dv but dF/dz is no good.
How can I get rid of those derivatives?