Derivative of e^2x with respect to e^x is:

The correct answer is Option (2) → $2e^x$ ##

Let $u = e^{2x}, v = e^x$.

$\frac{du}{dx} = e^{2x} \cdot 2, \quad \frac{dv}{dx} = e^x$

$\frac{du}{dv} = \frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2e^{2x}}{e^x} = 2e^x$