Y=(x-1)e^arctanx的导数

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Y=(x-1)e^arctanx的导数Y=(x-1)e^arctanx的导数Y=(x-1)e^arctanx的导数y''=e^arctanx+(x-1)e^(arctanx)/(1+x^2)=e^arc

Y=(x-1)e^arctanx的导数
Y=(x-1)e^arctanx的导数

Y=(x-1)e^arctanx的导数
y' = e^arctanx + (x-1) e^(arctanx) /(1+x^2)
= e^arctanx [ (x+x^2) / (1+x^2) ]

分部求导
Y'=(x-1)' e^arctanx+(x-1)(e^arctanx)'
=-e^arctanx+(x-1)e^arctanx (arctanx )'
=-e^arctanx+(1/x) (x-1)e^arctanx
=(x-1) /x e^arctanx -e^arctanx
=(1/x-2)e^arctanx