# How do you find (dy)/(dx) given 4xy+4x+3=0?

Nov 3, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1 + y}{x}$

#### Explanation:

I propose a slightly different approach.

$4 x y = - 3 - 4 x$

$x y = \frac{- 3 - 4 x}{4}$

Now, differentiate with respect to $x$.

$y + x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = \frac{- 4 \times 4 - 0 \times \left(- 3 - 4 x\right)}{4} ^ 2$

$y + x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = - \frac{16}{16}$

$y + x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = - 1$

$x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = - 1 - y$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 1 - y}{x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1 + y}{x}$

Hopefully this helps!