The original equation is this:

2x^2 -3y^2 = 0

(2x^2 -3y^2)' = (0)'

4x - 6y(dy/dx) = 0

I got the first derivative....which is correct according to my solutions manual: (2x/3y)

I took the derivative of this:

4x - 6y(dy/dx) = 0

(4x - 6y(dy/dx))' = (0)'

and got this using the product rule:

(6y)' ..... 6(dy/dx)

(dy/dx)....(dy/dx)^2

4 - 6(dy/dx)*(dy/dx) - 6y*(dy/dx)^2 = 0 ----> correct according the solutions manual

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This is where I went wrong....

I tried to isolate (dy/dx)^2 here:

4 = 6(dy/dx)^2 + 6y(dy/dx)^2

4 = [(dy/dx)^2][(6)(1+y)]

dividing out [(6)(1+y)]

2/3(1+y)=(dy/dx)^2

This is how the solutions manual does it:

(dy/dx)^2 = - (3)(dy/dx)^2 -2 / 3y

=2(3y^2-2x^2)/9y^3

= - (8/9y^3)What did I do wrong when trying to isolate (dy/dx)^2 ???

Also ... a side question... is there an easier way to type out this stuff? Like a program I can use?

Thank you to whoever answers this....I have been trying to figure this out for like 2 hours