http://i43.tinypic.com/261dxqe.jpg
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.
Thanks!
http://i43.tinypic.com/261dxqe.jpg
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.
Thanks!
Ok, move the y to the other side of the equals sign so that you get this:
$\displaystyle xy^2 -xy + x - y = 0$
Now, implicitly derive (i'll group each piece)
$\displaystyle (y^2 + 2xyy') - (y + xy') + 1 - y' = 0$
Now you move y^2 - y + 1 to the other side of the equals sign
$\displaystyle 2xyy' + xy' - y' = -(y^2 - y + 1)$
Now factor out y'
$\displaystyle y'(2xy + x - 1) = -(y^2 - y + 1)$
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.