设x=t2+2ty=2t3+3t2确定函数y=y(x),求d2ydx2=______

设x=t2+2ty=2t3+3t2确定函数y=y(x),求d2ydx2=______.
2025-12-18 03:46:09
推荐回答(1个)
回答1:

因为

x=t2+2t
y=2t3+3t2

所以
dx
dt
=2t+2
dy
dt
=6t2+6t

所以
dy
dx
dy
dt
dx
dt
t+1
3t2+3t

所以
d2y
dx2
d
dx
(
dy
dx
)=
d
dt
(
dy
dx
)
dt
dx
=
d
dt
(
dy
dx
)
1
dx
dt

=
3t2+3t?(6t+3)(t+1)
(3t2+3t)2
?
1
6t2+6t

=
?3t2?6t?3
2×27(t2+1)3

=-
(t+1)2
18(t2+1)3

故答案为:?
(t+1)2
18(t2+1)3