Question

consider a curve described by F(x,y(x))=0. By differentiating both sides of this expression using the First Version of the Chain Rule, show that dy/dx=-(∂F/∂x)/(∂F/∂y)

Answer 1

Well, dF/dx = 0 because F itself is a constant.

And

dF/dx = (∂F/∂x) + (∂F/∂y) dy/dx

Hence
(∂F/∂x) + (∂F/∂y) dy/dx = 0
=> dy/dx = -(∂F/∂x)/(∂F/∂y)

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