设x=f′(t)y=tf′(t)?f(t),且f″(t)≠0,f′″(t)存在,求d2ydx2、d3ydx3

2025-03-10 14:51:20
推荐回答(1个)
回答1:

由于
dx
dt
=f″(t)
dy
dt
=tf″(t)

dy
dx
dy
dt
dx
dt
=t

d2y
dx2
d
dx
(
dy
dx
)=
d
dt
(
dy
dx
)
dt
dx
dt
dx
=
1
f″(t)

d3y
dx3
d
dt
(
1
f″(t)
)
dt
dx
=?
f″′(t)
[f″(t)]3