How do you use implicit differentiation to find dy/dx given x^2+y^2+3x-4y=9?

1 Answer
Sep 16, 2016

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

Explanation:

${x}^{2} + {y}^{2} + 3 x - 4 y = 9$

Using implicit differentiation:
$2 x + 2 y \frac{\mathrm{dy}}{\mathrm{dx}} + 3 - 4 \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

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

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