Si $y = \tan^{-1} \sqrt{\frac{x+1}{x-1}}$, determinar $\frac{dy}{dx}$:

• [a.] $\frac{-1}{2|x|\sqrt{x^2-1}}$
• [b.] $\frac{-1}{2x\sqrt{x^2-1}}$
• [c.] $\frac{1}{2x\sqrt{x^2-1}}$
• [d.] none of these