Question

f(lnx+1)=e^x+3x 求df(x)/dx

Answer 1

f(lnx+1)=e^x+3x

u=lnx+1,x=e^(u-1)

f(u)=e^[e^(u-1)]+3e^(u-1)

f(x)=e^[e^(x-1)]+3e^(x-1)

df/dx=e^[e^(x-1)]*e^(x-1)*1+3e^(x-1)*1

=e^[e^(x-1)]*e^(x-1)+3e^(x-1)

你第一项复合函数求导没有乘以指数上的e^(x-1)的导数