Let f: R → R be a differentiable function satisfying f^′(3)+f^′(2)=0. Then lim_x → 0((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) is equal to:

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a differentiable function satisfying $\displaystyle f^{\prime}(3)+f^{\prime}(2)=0$. Then $\displaystyle \lim _{x \rightarrow 0}\left(\frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)}\right)^{\frac{1}{x}}$ is equal to :