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

Jun 10, 2018

$\setminus \frac{\mathrm{dy}}{\mathrm{dx}} = - \setminus \frac{3 {x}^{2}}{4 y}$

#### Explanation:

Differentiate both sides as such:
$\setminus \frac{d}{\mathrm{dx}} \left(- 2 {y}^{2} + 3\right) = \setminus \frac{d}{\mathrm{dx}} \left({x}^{3}\right)$
$- 2 \setminus \frac{d}{\mathrm{dx}} \left({y}^{2}\right) = 3 {x}^{2}$
$- 2 \left(2 y \setminus \frac{\mathrm{dy}}{\mathrm{dx}}\right) = 3 {x}^{2}$
rearrange to make $\setminus \frac{\mathrm{dy}}{\mathrm{dx}}$ the factor to get:
$\setminus \frac{\mathrm{dy}}{\mathrm{dx}} = - \setminus \frac{3 {x}^{2}}{4 y}$