# How do you find the derivative of ((1+3x)/(3x))(3-x)?

Jan 27, 2017

$- 1 - \frac{1}{x} ^ 2$

#### Explanation:

Combine the numerator by multiplying so that it is $\frac{- 3 {x}^{2} + 8 x + 3}{3 x}$

Now apply the quotient rule to differentiate or proceed as follows:

$\frac{- 3 {x}^{2} + 8 x + 3}{3 x}$ =$- x + \frac{8}{3} + \frac{1}{x}$

Now differentiate term wise = $- 1 - \frac{1}{x} ^ 2$