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x
(5)yeaxsi
bx,求dy答案:yeaxsi
bxeaxsi
bx
aeaxsi
bxeaxcosbxb
eaxasi
bxbcosbx
3
fdyeaxasi
bxbcosbxdx
(6)yexx
1
x,求dy
311答案:dyx2exdx2x
(7)ycos
xex
2
2
,求dy
2xdx
答案:dy2xex

si
x
(8)ysi
xsi
x,求y答案:y
si
1xcosx
cos
x
si
1xcosxcos
x(9)yl
x答案:y
1x2,求y
1x1x
1
2
x1x2
11211x22x22x1x

1x1x2
1
x1x2


11x2
cot1x
(10)y2

1x
13x22xx
l
2cosx2
,求y
答案:y
2
si

153x1x21x626
4下列各方程中y是x的隐函数,试求y或dy(1)x2y2xy3x1,求dy答案:解:方程两边关于X求导:
4
f2x2yyyxy30
2yxyy2x3

dy
y32xdx2yx
(2)si
xyexy4x,求y答案:解:方程两边关于X求导:
cosxy1yexyyxy4cosxyexyxy4yexycosxy
y4yexycosxyxexycosxy
5.求下列函数的二阶导数:(1)yl
1x2,求y答案:y
22x21x22
(2)y1x,求y及y1
x
答案:y3x
4

52

12x,y114
3
电大《经济数学基础》形成性考核册2及参考答案(一)填空题
_________1若fxdx2x2xc,则fx__________答案:2xl
22
2si
xdx________答案:si
xc3若fxdxFxc,则exfexdx4设函数
del
1x2dx___________答案:01dx
0
答案:Fexc
5若Pxx
11t
2
dt,则Px__________答案:
11x2
5
f(二)单项选择题1下列函数中,(A.1cosx
2
2
D
)是xsi
x的原函数.B.2cosx
2
2
C.2cosx
2
D.1cosx
2
2
2下列等式成立的是(A.si
xdxdcosxC.2xdx
1d2xl
2
C).B.l
xdxd1
x
D.
1x
dxdx
3下列不定积分中,常用分部积分法计算的是(A.cos2x1dx,
1
C
).D.
xdx1x2
B.x
1x2dx
C.xsi
2xdxD).B.1
16
4下列定积分计算正确的是(A.12xdx2C.x2x3dx0

dx15
D.si
xdx0
5下列无穷积分中收敛的是(B).Ar
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