Question

вычеслите производную плиз
$y = \frac{ \times ^{2} - 1}{x {}^{2} + 1}$

Answer 1

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

Answer 2

найти производную функции $\mathtt{f(x)}$, если $\mathtt{f(x)=1-\frac{2}{x^2+1}}$

$\mathtt{f'(x)=-2[(x^2+1)^{-1}]'=2(x^2+1)^{-2}(x^2+1)'=\frac{4x}{(x^2+1)^2}}$