用对数求导法：对
y = (2 ln x + x^2)/(3lnx + x^2)
两边取对数,得
lny = ln(2 ln x + x^2) - ln(3lnx + x^2),
两边关于 x 求导数,得
y'/y = (2/x+2x)/(2 ln x + x^2) - (3/x+2x)/(3lnx + x^2),
因此,答案是
y' = y[(2/x+2x)/(2 ln x + x^2) - (3/x+2x)/(3lnx + x^2)],
整理化简就留给你了.