求y=x/1-x的二阶导数还有y=ln[f(e^x)]的二阶导数

Question

求y=x/1-x的二阶导数还有y=ln[f(e^x)]的二阶导数

Answer 1

y=x/(1-x)=-1-1/(x-1)
y'=1/(x-1)^2
y''=-2/(x-1)^3
y=ln[f(e^x)]
y'=f'(e^x)/f(e^x)*(e^x)=e^xf'(e^x)/f(e^x)
y''={[e^xf'(e^x)]'f(e^x)-[f(e^x)]'[e^xf'(e^x)]}/f^2(e^x)
=[e^xf(e^x)f'(e^x)+e^(2x)f(e^x)f''(e^x)-e^(2x)f''(e^x)]/f^2(e^x)