用對數(shù)求導(dǎo)法：對
y = (2 ln x + x^2)/(3lnx + x^2)
兩邊取對數(shù),得
lny = ln(2 ln x + x^2) - ln(3lnx + x^2),
兩邊關(guān)于 x 求導(dǎo)數(shù),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)],
整理化簡就留給你了.