Question

решите,пожалуйста))))

Answer 1

$1); ; y= frac{1-x^2}{1+x^2}\\y'=frac{-2x(1+x^2)-(1-x^2)cdot 2x}{(1+x^2)^2}=frac{-2x-2x^3-2x+2x^3}{(1+x^2)^2}=-frac{4x}{(1+x^2)^2}\\2); ; y=sin(x^2+1)\\y'=cos(x^2+1)(x^2+1)'=cos(x^2+1)cdot 2x\\y''=-sin(x^2+1)cdot underbrace {(x^2+1)'}_{2x}cdot 2x+cos(x^2+1)cdot 2=\\=-4xcdot sin(x^2+1)+2cdot cos(x^2+1)\\3); ; y=x^2-8x+12\\y'=2x-8qquad znaki; y':; ---underbrace {(4)}_{y'(4)=0}+++\\2x-8 textgreater 0\\2x textgreater 8\\x textgreater 4\\y(x); ; vozrastaet; pri; xin [, 4,+infty )$