Math - How Do You Solve This?

[biobiobio]

Just push me in the right direction... Methods, hints...

I would have asked about questions like this in the math help centre earlier, if it wasn't full.. -.-

 

Find y'.

Could you use implicit differentiation?

Thank you!

[lawcat]

 

Could you use implicit differentiation?

Thank you!

Yes

[Qfwfq]

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.