求下列隐函数的导数：y=x*(e^y)+2 e^y=sin(x+y)y=x*(e^y)+2和e^y=

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y = xe^y + 2
y' = e^y + xe^y * y'
y' * (1 - xe^y) = e^y
y' = e^y/(1 - xe^y)
y' = 1/[e^(- y) - x]
e^y = sin(x + y)
e^y * y' = cos(x + y) * (1 + y')
e^y * y' = cos(x + y) + y' * cos(x + y)
y' * [e^y - cos(x + y)] = cos(x + y)
y' = cos(x + y)/[e^y - cos(x + y)]
y' = 1/[e^ysec(x + y) - 1]
======以下答案可供参考======
供参考答案1:
额供参考答案2:
第一个，y=x*(e^y)+2
方法① 原式等于： y-2=x*(e^y)
两边取对数得 ln(y-2)=y+lnX
ln(y-2)-y=lnX
两边对x求导1/(y-2)y'-y'=1/x
y'=(y-2)/[x*(y+3)]
方法②两边对X求导得 y'=e^y+x*e^y*y'
y'*(1-xe^y)=e^y
y'=e^y/(1-xe^y)
第二个，e^y=sin(x+y)
两边对x求导得 e^y*y'=cos(x+y)*(1+y')
e^y*y'-cos(x+y)*y'=cos(x+y)
y'=cos(x+y)/[e^y-cos(x+y)]