Question

Вычеслить производную!!

Answer 1

$y=x+ln\frac{x-\sqrt2}{x+\sqrt2}\\\\y'=1+\frac{x+\sqrt2}{x-\sqrt2}\cdot \frac{1\cdot (x+\sqrt2)-(x-\sqrt2)\cdot 1}{(x+\sqrt2)^2}=1+\frac{x+\sqrt2}{x-\sqrt2}\cdot \frac{2\sqrt2}{(x+\sqrt2)^2}=\\\\=1+\frac{2\sqrt2}{(x-\sqrt2)(x+\sqrt2)}=1+\frac{2\sqrt2}{x^2-2}\\\\oo$