# What is the derivative of (3y)/(2x)?

Feb 4, 2018

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

#### Explanation:

Applying linearity and the quotient rule we have:

$\frac{d}{\mathrm{dx}} \left(\frac{3 y}{2 x}\right) = \frac{3}{2} \setminus \frac{d}{\mathrm{dx}} \left(\frac{y}{x}\right)$

$\text{ } = \frac{3}{2} \setminus \frac{\left(x\right) \left(\frac{d}{\mathrm{dx}} y\right) - \left(y\right) \left(\frac{d}{\mathrm{dx}} x\right)}{x} ^ 2$

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