设y=f(x+y),其中f具有二阶导数,且其一阶导数不等于1,求d2ydx2.

问题描述:

设y=f(x+y),其中f具有二阶导数,且其一阶导数不等于1,求

d2y
dx2

设u=x+y,则y=f(u)∴dydx=f′(u)dudx=f′(u)(1+dydx)解得:dydx=f′(u)1−f′(u)∴d2ydx2=ddx(f′(u)1−f′(u))=ddu(f′(u)1−f′(u))•dudx=f″(u)[1−f′(u)]+f′(u)f″(u)[1−f′(u)]2•(1+f′(u)1−f′(u...