# What is the derivative of e^(2x)/x?

Jul 20, 2016

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

#### Explanation:

so why not use the quotient rule

$\left(\frac{u}{v}\right) ' = \frac{u ' \cdot v - u \cdot v '}{{v}^{2}}$

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

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