设z=v⼀u而u=lnx v=e^x求dz⼀dx的全导数

2024-12-19 18:46:29
推荐回答(3个)
回答1:

详情如图所示,

有任何疑惑,欢迎追问

回答2:

  1. dz/dx=∂z/∂u du/dx + ∂z/∂v dv/dx

  2. = -v/xu² + e^x /u

  3. = -e^x/xln²x + e^x / lnx

  4. = e^x(1 - 1/lnx )/ lnx 

回答3:

[㏑f(x)]'=[v(x)·㏑u(x)]'
f'(x)/f(x)=v'(x)·㏑u(x)+v(x)u'(x)/u(x)
y'/y=v'(x)·㏑u(x)+v(x)u'(x)/u(x)
y'=y[v'(x)·㏑u(x)+v(x)u'(x)/u(x)]
=u(x)^v(x)[v'(x)·㏑u(x)+v(x)·u'(x)/u(x)]