u(x)=lnx,v(x)=e^x 求(uv)的三阶微分

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 00:20:34
u(x)=lnx,v(x)=e^x求(uv)的三阶微分u(x)=lnx,v(x)=e^x求(uv)的三阶微分u(x)=lnx,v(x)=e^x求(uv)的三阶微分u=lnxu''=1/xu''''=-1/x

u(x)=lnx,v(x)=e^x 求(uv)的三阶微分
u(x)=lnx,v(x)=e^x 求(uv)的三阶微分

u(x)=lnx,v(x)=e^x 求(uv)的三阶微分
u=lnx
u'= 1/x
u'' = -1/x^2
u'''= 2/x^3
v = e^x
v'=v''=v'''=e^x
(uv)' =uv'+u'v
(uv)'' = uv''+2u'v'+u''v
(uv)''' = uv'''+3u'v''+3u''v'+u'''v
=(lnx)e^x+ 3e^x/x- 3e^x/x^2 + 2e^x/x^3