数学问题怎么解
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
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