# Question #cde8d

##### 2 Answers
Sep 29, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16 {x}^{2} + 15 y}{15 x + 6 y}$

#### Explanation:

$8 {x}^{2} + 15 x y + 3 {y}^{2} = 15$
Differentiating w.r.t. x,
$16 {x}^{2} + 15 y + 15 x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) + 6 y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = 0$
$16 {x}^{2} + 15 y + \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) \left(15 x + 6 y\right) = 0$

Sep 29, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16 x + 15 y}{15 x + 6 y}$

#### Explanation:

$\text{differentiate "color(blue)"implicitly with respect to x}$

$\text{differentiate "15xy" using the "color(blue)"product rule}$

$\Rightarrow 16 x + 15 \left(x \frac{\mathrm{dy}}{\mathrm{dx}} + y\right) + 6 y \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\Rightarrow 16 x + 15 x \frac{\mathrm{dy}}{\mathrm{dx}} + 15 y + 6 y \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} \left(15 x + 6 y\right) = - 16 x - 15 y$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16 x + 15 y}{15 x + 6 y}$