# Math Help - Implicit Differentiation

1. $x^2-xy-4y^2=0$
Find: $(dy)/(dx)$

$
(dy)/(dx)=(y+10x)/(x+8y)
$

and i just want to make sure I did it right...

2. Edit: Oh you just had to get banned. =p

$x^2 - xy - 4y^2 = 0$

$(2x) - (y + xy') - (8yy') = 0$

$2x - y - xy' - 8yy' = 0$

$(xy' + 8yy') = (2x - y)$

$y'(x + 8y) = (2x - y)$

$y' = \frac{2x - y}{x + 8y}$

Easier way to do it when you've got it in that form: -(d/dx)/(d/dy)

d/dx = 2x - y
d/dy = -x - 8y

$\frac{-(d/dx)}{(d/dy)} = \frac{-(2x - y)}{-x - 8y} = \frac{2x - y}{x + 8y}$