# How do you find the derivative of F(x) = 1/(x-5)?

##### 1 Answer
Mar 18, 2016

$\frac{\mathrm{dF}}{\mathrm{dx}} = \frac{- 1}{x - 5} ^ 2$

#### Explanation:

Let
$u = 1$
$v = x - 5$

We know, Quotient Rule

$\frac{v \frac{d}{\mathrm{dx}} u - u \frac{d}{\mathrm{dx}} v}{v} ^ 2$

$\frac{\left(x - 5\right) \frac{d}{\mathrm{dx}} 1 - 1 \frac{d}{\mathrm{dx}} \left(x - 5\right)}{x - 5} ^ 2$

$\frac{\left(x - 5\right) \cdot 0 - 1 \cdot 1}{x - 5} ^ 2 = \frac{- 1}{x - 5} ^ 2$

This will be the answer of the differentiated function.