I'm not sure how to solve this problem:

Suppose h:R^2--->R is of class C^1 and dh/dx2 =/=0. Show that the equation h(y/x, z/x)=0 defines z (locally) implicitly as a C^1 function z=f(x,y) and show that x*df/dx + y*df/dy = f(x,y).

Thanks

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- October 30th 2009, 12:36 PMAKTiltedShowing an equation defines a function implicitly
I'm not sure how to solve this problem:

Suppose h:R^2--->R is of class C^1 and dh/dx2 =/=0. Show that the equation h(y/x, z/x)=0 defines z (locally) implicitly as a C^1 function z=f(x,y) and show that x*df/dx + y*df/dy = f(x,y).

Thanks