数学问题怎么解

更新时间2019-12-27 00:40:04

大家请帮我一下,函数y'=(-y)/(e^y+x)怎样继续一次求导,请写出详细步骤.

y'' = [ -y' +(e^y+x) + y( y'e^y+1) ]/(e^y+x)^2

= { [ y/(e^y+x) ] * (e^y+x) + ye^y[ (-y)/(e^y+x) ] + y }/(e^y+x)^2

= 2y/(e^y+x)^2 - y^2e^y/(e^y+x)^3 .

用公式：(u/v)'=(u'v-uv')/v²

y'=-y/(e^y+x)

y''=-[y'(e^y+x)-y(y'e^y+1)]/(e^y+x)²

=-[-y-y(y'e^y+1)]/(e^y+x)²

=y(y'e^y+2)/(e^y+x)²

=y[-ye^y+2(e^y+x)]/(e^y+x)³

=(-y²e^y+2ye^y+2xy)/(e^y+x)³