# How do you implicitly differentiate x y + 2x + 3x^2 = 4?

Dec 2, 2015

You can do it like this:

#### Explanation:

$x y + 2 x + 3 {x}^{2} = 4$

$\therefore D \left(x y + 2 x + 3 {x}^{2}\right) = D \left(4\right)$

$\therefore x y ' + y + 2 + 6 x = 0$

$\therefore - x y ' = 6 x + 2 + y$

$\therefore y ' = - \frac{\left(6 x + 2 + y\right)}{x}$