Evaluating a limit with variable in the exponent For
$$\lim_{x \to \infty} \left(1- \frac{2}{x}\right)^{\dfrac{x}{2}}$$ 
I have to use the L'Hospital"s rule, right? So I get:
$$\lim_{x \to \infty}\frac{x}{2} \log\left(1- \frac{2}{x}\right)$$
And what now? I need to take the derivative of the log, is it:
$\dfrac{1}{1-\dfrac{2}{x}}$  but since there is x, I need to use the chain rule  multiply by the derivative of $\dfrac{x}{2}$  ? 

Recall the limit:
$$\lim_{y \to \infty} \left(1+\dfrac{a}y\right)^y = e^a$$
I trust you can finish it from here, by an appropriate choice of $a$ and $y$.
