I explained here^...this is just a practice quiz but I'm not sure if I have the right answer and they messed up the choices, OR if mine is just wrong.
Ok, move the y to the other side of the equals sign so that you get this:
Now, implicitly derive (i'll group each piece)
Now you move y^2 - y + 1 to the other side of the equals sign
Now factor out y'
And finally divide by (2xy + x - 1)
If you noticed, what you essentially did was move d/dx to the other side of the equals sign and divide d/dy.
Hence -(d/dx)/(d/dy) being the shortcut to implicitely deriving.