问答题
设y=X2eh，求y
(n)
．
【正确答案】正确答案：用莱布尼兹法则并注意(x
2
)
(k)
=0(k=3，4，…)， (e
2x
)
(k)
=2
k
e
2x
，得 y
(n)
)=
C
n
k
(x
2
)
(k)
(e
2x
)
(n—k)
=x
2
(e
2x
)
(n)
+n(x
2
)'(e
2x
)
(n—1)
+
(x
2
)"(e
2x
)
(n—2)
=2
n
e
2x
[x
2
+nx…+
C
n
k
(x
2
)
(k)
(e
2x
)
(n—k)
=x
2
(e
2x
)
(n)
+n(x
2
)'(e
2x
)
(n—1)
+
(x
2
)"(e
2x
)
(n—2)
=2
n
e
2x
[x
2
+nx…+
【答案解析】