Question

Y=(x^2-1)/(x^2 +1) найти производную функции.

Answer 1

$y'=(\frac{x^2-1}{x^2+1})'=\frac{(x^2-1)'(x^2+1)-(x^2-1)(x^2+1)'}{(x^2+1)^2}= \frac{2x(x^2+1)-2x(x^2-1)}{x^4+2x^2+1} \\=\frac{2x^3+2x-2x^3+2x}{x^4+2x^2+1}=\frac{4x}{x^4+2x^2+1}$