Implicit Differentiation: Solving for dy/dx

[la_med12]

1.
I'm pretty sure I've got this right.. just needing a check. Cheers!

2.
x^2+2xy-y^2+x^2=2

3.
2x+2x(dy/dx)+2y-2y(dy/dx)+2x=0
2x(dy/dx)-2y(dy/dx)=-4x-2y
dy/dx(2x-2y)=-4x-2y
dy/dx=(-4x-2y)/(2x-2y)

 

[Maybe_Memorie]

Correct, but you can factorise and multiply top and bottom by -1 to become
$$\frac{dy}{dx} = \frac{y+2x}{y-x}$$
which looks nicer.

 

[la_med12]

Thanks for the check.

Cheers!