题目

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=sin(x+y)求这两题过程

提问时间：2020-10-18

答案

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]