# How do you differentiate  -(2/(3x)) ?

May 29, 2016

See below for two solutions.

#### Explanation:

If you want to use the quotient rule , you can.

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

$= - \left[\frac{\left(0\right) 3 x - 2 \left(3\right)}{3 x} ^ 2\right]$

$= - \left[\frac{- 6}{9 {x}^{2}}\right] = \frac{6}{9 {x}^{2}} = \frac{2}{3 {x}^{2}}$

Alternatively , you can rewrite the expression before differentiating.

$\frac{d}{\mathrm{dx}} \left(- \frac{2}{3 x}\right) = \frac{d}{\mathrm{dx}} \left(- \frac{2}{3} {x}^{-} 1\right)$

Now use the power and constant multiple rules.

$= \left(- 1\right) \left(- \frac{2}{3}\right) {x}^{- 1 - 1} = \frac{2}{3} {x}^{-} 2 = \frac{2}{3 {x}^{2}}$

Use whichever method you like.