y ' = 1/(x+根号(x²+1) * [1 + 2x/根号(x²+1) ]
y' = 2x*e^(x²) - e^(-x)
y² - xy + x²-1 = 0 y = -x+根号(4-3x²)]/2 ,或 y = [-x-根号(4-3x²)]/2
因为图像过点(0,1),也过点(0,-1)
y ' = -1/2 + (1/2) * (1/2)*(-6x)*1/根号(4-3x²)
当x = 0时,y ' = -1/2
所以过点(0,1)处的切线方程是:y = -x/2 + 1
y ' = 3x² - 6x = 0 x = 0, x = 2.
y '' = 6x -6 当x = 0 时 y '' < 0, y = 7. 当x = 2时,y '' > 0,y = 3
所以当x>2或 x<0时y ' > 0, y 单调递增,当0<=x<=2时y'<0,y单调递减。