Найти производную второго порядка: 1) sin(x)/(1+sin(x)) 2) xsin(x^3) 4) Частные...

1) y(x) = sin x/(sin x + 1) = (sin x + 1 - 1)/(sin x + 1) = 1 - 1/(sin x + 1)
$y'= 0-\frac{0-1*cos(x)}{(sin(x)+1)^2} =\frac{cos(x)}{(sin(x)+1)^2}$

2) y = x*sin(x^3)
y' = 1*sin(x^3) + x*cos(x^3)*3x^2 = sin(x^3) + 3x^3*cos(x^3)

3) u = (x+y)/(x^2+y^2)
$\frac{du}{dx} = \frac{1(x^2+y^2) - (x+y)*2x}{(x^2+y^2)^2} = \frac{-x^2-2xy+y^2}{(x^2+y^2)^2}$
$\frac{du}{dy} = \frac{1(x^2+y^2) - (x+y)*2y}{(x^2+y^2)^2}= \frac{x^2-2xy-y^2}{(x^2+y^2)^2}$