$$y=\frac{2x}{x^2-1}$$

$$y=\frac{2x}{x^2-1}=\frac{u}{v}$$

$$u=2x ; u^{\text{'}}=2$$

$$v=x^2-1 ; v^{\text{'}}=2x$$

$$y^{\text{'}}=\frac{u^{\text{'}}v-u{v}^{\text{'}}}{v^2}$$

$$y^{\text{'}}=\frac{2·\left(x^2-1\right)-2x·2x}{{\left(x^2-1\right)}^2}$$

$$y^{\text{'}}=\frac{2x^2-2-4x^2}{{\left(x^2-1\right)}^2}$$