Let $$f(x) = \int_0^x e^t f(t)dt + e^x$$ be a differentiable function for all $$x \in R$$. Then $$f(x)$$ equals:

A

$$e^{(e^x - 1)}$$

B

$$e^{e^x} - 1$$

C

$$2e^{e^x} - 1$$

D

$$2e^{(e^x - 1)} - 1$$