# How do you find the derivative for y=(3x)/(x+5)?

Jun 11, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{15}{x + 5} ^ 2$

#### Explanation:

$y = \frac{3 x}{x + 5}$

$y = 3 \times \frac{x}{x + 5}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 \times \frac{\left(x + 5\right) \left(1\right) - \left(x\right) \left(1\right)}{x + 5} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 \times \frac{x + 5 - x}{x + 5} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 \times \frac{5}{x + 5} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{15}{x + 5} ^ 2$

The quotient rule is given by:
$y = \frac{u}{v}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{v u ' - u v '}{v} ^ 2$