Let f be a real-valued function defined on the interval (-1, 1) such that $$e^{-x}f(x) = 2 + \int_{0}^{x}\sqrt{t^4 + 1} dt$$, for all $$x \in (-1, 1)$$, and let $$f^{-1}$$ be the inverse function of f. Then $$(f^{-1})'(2)$$ is equal to

A

1

B

$$\frac{1}{3}$$

C

$$\frac{1}{2}$$

D

$$\frac{1}{e}$$