(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The determinant J (^{f,g}/_{u,v}) =|∂f/∂u ∂f/∂v

∂g/∂u ∂g/∂v |:

if z = f(x,y) and g(x,y) = 0, show that dz/dx =^{∂f/∂x*∂g/∂y - ∂f/∂y * ∂g/∂x}/_{∂g/∂y}=^{1}/_{∂g/∂y}J(f,g/x,y)

2. Relevant equations

∂z/∂x = ∂z/∂f*∂f/∂x

∂z/∂x = ∂z/∂g*∂g/∂x

∂z/∂y = ∂z/∂f*∂f/∂y

∂z/∂y = ∂z/∂g*∂g/y

3. The attempt at a solution

should u be placed in the f function and v in the g function? So it may be f(u), g(v) = 0. need some tips please

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# Partial differentiation -higher order

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