# How do you find the derivative of f(x)= (2x^2-x+1)/(2x-1) using the quotient rule?

Jun 14, 2015

$y ' = \frac{4 {x}^{2} - 4 x - 1}{2 x - 1} ^ 2$.

#### Explanation:

In this way:

$y ' = \frac{\left(4 x - 1\right) \left(2 x - 1\right) - \left(2 {x}^{2} - x + 1\right) \cdot 2}{2 x - 1} ^ 2 =$

$= \frac{8 {x}^{2} - 4 x - 2 x + 1 - 4 {x}^{2} + 2 x - 2}{2 x - 1} ^ 2 =$

$= \frac{4 {x}^{2} - 4 x - 1}{2 x - 1} ^ 2$.