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  • 求下列隱函數(shù)的導(dǎo)數(shù):y=x*(e^y)+2 e^y=sin(x+y)

    求下列隱函數(shù)的導(dǎo)數(shù):y=x*(e^y)+2 e^y=sin(x+y)
    y=x*(e^y)+2和e^y=sin(x+y)求這兩題過(guò)程
    數(shù)學(xué)人氣:737 ℃時(shí)間:2020-04-09 12:46:06
    優(yōu)質(zhì)解答
    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]
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