A function f(x)f(x)f(x) is defined by the integral f(x)=∫x2xettdtf(x) = \int_{x}^{2x} \frac{e^{t}}{t} dtf(x)=∫x2xtetdt. Determine the derivative f′(x)f'(x)f′(x) for x>0x > 0x>0.
e2x−exx\frac{e^{2x} - e^x}{x}xe2x−ex
e2x+ex2x\frac{e^{2x} + e^x}{2x}2xe2x+ex
2e2x−exx\frac{2e^{2x} - e^x}{x}x2e2x−ex
e2x−2ex2x\frac{e^{2x} - 2e^x}{2x}2xe2x−2ex