微积分 还有几道,能否也帮我做一下,太感谢啊

2025-05-13 07:12:01
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回答(1):

8题:较简单的办法是求对数后求导
lny=ln(x+1)+2ln(x+2)+3ln(x+3)
两边求导得:y'/y=1/(x+1)+2/(x+2)+3/(x+3)
所以:y'=(x+1)(x+2)^2*(x+3)^3*(1/(x+1)+2/(x+2)+3/(x+3))
9:两边对x求导得:
2x+y+xy'=(y+xy')/(1+x^2*y^2)
所以:y'=((2x+y-y/(1+x^2*y^2))/(x+x/(1+x^2*y^2))
=(2+2x^2*y^2+xy^3)/(2+2x^2*y^2)