Question

-3.x² – 3y² +12x - 5y +6=0

Answer 1

Respuesta:

$\frac{dy}{dx} = \frac{12 - 6x}{6y + 5}$

Explicación paso a paso:

$- 3 \times {x}^{2} - 3 {y}^{2} + 12x - 5y + 6 = 0$

$- \frac{d}{dx} (3 {x}^{2}) - \frac{d}{dx} (3 {y}^{2}) + \frac{d}{dx}(12x) - \frac{d}{dx}(5y) + \frac{d}{dx}(6) = \frac{d}{dx}(0)$

$- \frac{d}{dx} (3 {x}^{2}) - \frac{d}{dx} (3 {y}^{2}) + \frac{d}{dx}(12x) - \frac{d}{dx}(5y) + 0 = 0$

$- 3 \times \frac{d}{dx}( {x}^{2} ) - \frac{d}{dy}(3 {y}^{2} ) \times \frac{d}{dx} + 12 - \frac{d}{dy}(5y) \times \frac{dy}{dx} = 0$

$- 3 \times 2x - 3 \times \frac{d}{dy} ( {y}^{2} ) \times \frac{dy}{dx} + 12 - 5 \times \frac{dy}{dx} = 0$

$- 6x - 3 \times 2y \times \frac{dy}{dx} + 12 - 5 \times \frac{dy}{dx} = 0$

$- 6x - 6y \times \frac{dy}{dx} + 12 - 5 \times \frac{dy}{dx} = 0$

$- 6y \times \frac{dy}{dx} - 5 \times \frac{dy}{dx} = 6x - 12$

$( - 6y - 5) \times \frac{dy}{dx} = 6x - 12$

$\frac{dy}{dx} = \frac{6 \times - 12}{ - 6y - 5}$

$\frac{dy}{dx} = \frac{12 - 6x}{6y + 5}$