Find the derivative of $\dfrac{e^{2x}}{x}$

The correct answer is $\dfrac{(2x - 1)e^{2x}}{x^2}$

As per Quotient Rule,

$\dfrac{dy}{dx}$ = $\dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx}}{v^2}$


$ ∴ \dfrac{dy}{dx}$ = $\dfrac{(x) D(e^{2x}) - (e^{2x}) D(x)}{x^2}$


= $\dfrac{x (2 e^{2x}) - (e^{2x})(1)}{x^2}$


= $\dfrac{(2x - 1)e^{2x}}{x^2}$