Question

Найти производную f(x)=(x+1/x+2)^2

Answer 1

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