# How do you find the derivative of (x-3) /( 2x+1)?

Jun 16, 2018

$\frac{d}{\mathrm{dx}} \left(\frac{x - 3}{2 x + 1}\right) = \frac{7}{2 x + 1} ^ 2$

#### Explanation:

Using the quotient rule:

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

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

$\frac{d}{\mathrm{dx}} \left(\frac{x - 3}{2 x + 1}\right) = \frac{2 x + 1 - 2 x + 6}{2 x + 1} ^ 2$

$\frac{d}{\mathrm{dx}} \left(\frac{x - 3}{2 x + 1}\right) = \frac{7}{2 x + 1} ^ 2$