# How do you implicitly differentiate 2x^2+y^2=9xy-y?

Dec 8, 2015

You can do it like this:

#### Explanation:

$2 {x}^{2} + {y}^{2} = 9 x y - y$

$D \left(2 {x}^{2} + {y}^{2}\right) = D \left(9 x y - y\right)$

$\therefore 4 x + 2 y y ' = 9 \left(x y ' + y\right) - y '$

$\therefore y ' + 2 y y ' - 9 x y ' = 9 y - 4 x$

$\therefore y ' \left(2 y - 9 x\right) = 9 y - 4 x$

$\therefore y ' = \frac{\left(9 y - 4 x\right)}{\left(2 y - 9 x\right)}$