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Math - How Do You Solve This?


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After a few scribbles, the implicit function theorem is definitely the most straightforward way of doing it. They call it Dini's theorem, for short, here in Dini's land. :D

 

[math]y^3x^2-3y^4+3y-2x=f(x,y)=0[/math]

 

[math]\frac{dy}{dx}=-\frac{\frac{\partial f(x,y)}{\partial x}}{\frac{\partial f(x,y)}{\partial y}}[/math]

 

First, I had even thought of the trick, that in this case it's easy to write the two possible functions [imath]x(y)[/imath] so as to use the inverse rule, but nah, not much use and it would make for more forboding computations anyway.

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