# How do you find (dy)/(dx) given y^2+3x=2?

Oct 1, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{3}{2 \sqrt{2 - 3 x}}$

#### Explanation:

As ${y}^{2} + 3 x = 2$, we have

${y}^{2} = 2 - 3 x$ and $y = \sqrt{2 - 3 x}$

and using chain rule

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 \sqrt{2 - 3 x}} \times \left(- 3\right)$

= $- \frac{3}{2 \sqrt{2 - 3 x}}$