# What is the derivative of 1/(x-3)?

Sep 9, 2016

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

#### Explanation:

We have: $\frac{1}{x - 3}$

This expression can be differentiated using the "quotient rule":

$\frac{d}{\mathrm{dx}} \left(\frac{1}{x - 3}\right) = \frac{\left(x - 3\right) \cdot \left(0\right) - \left(1\right) \cdot \left(1\right)}{{\left(x - 3\right)}^{2}}$

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