Явное задание функции $$y(x)$$

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

$$y''=\:$$ $$\left ( \frac{2x}{\left ( 1 - x^{2} \right )^{2}} \right )'=\;$$ $$\frac{2\left ( 1 - x^{2} \right )^{2}-2x\cdot 2\cdot \left ( 1 - x^{2} \right )\cdot \left ( -2x \right )}{\left ( 1 - x^{2} \right )^{4}}=\;$$
$$=\frac{2\left ( 1 - x^{2} \right )+8x^{2}}{\left ( 1 - x^{2} \right )^{3}}=\;$$ $$2\cdot \frac{1+3x^{2}}{\left ( 1 - x^{2} \right )^{3}}=\;$$ $$-2\cdot \frac{1+3x^{2}}{\left ( x-1 \right )^{3}\cdot \left ( x+1 \right )^{3}}$$