Unit 4 Flashcards
(43 cards)
1
Q
d/dx(cu)
A
cu’
2
Q
d/dx(u +-v)
A
u’ +- v’
3
Q
d/dx(uv)
A
uv’+v’u
4
Q
d/dx(u/v)
A
(vu’-uv’)/v^2
5
Q
d/dx(c)
A
0
6
Q
d/dx(u^n)
A
n*u^(n-1)u’
7
Q
d/dx(x)
A
1
8
Q
d/dx(abs(u))
A
(u/abs(u))*u’ when u != 0
9
Q
d/dx(lnu)
A
u’/u
10
Q
d/dx(e^u)
A
(e^u)*(u’)
11
Q
d/dx(log base a of u)
A
u’/(lna * u)
12
Q
d/dx(a^u)
A
ln(a)(a^u)u’
13
Q
d/dx(sinx)
A
cosx*x’
14
Q
d/dx(cosx)
A
-(sinx)*u’
15
Q
d/dx(tanx)
A
sec^2(x)*x’
16
Q
d/dx(cotx)
A
-(csc^2(x))*x’
17
Q
d/dx(secx)
A
secxtanxu’
18
Q
d/dx(csc(x))
A
-csc(x)cot(x)x’
19
Q
d/dx(arcsin(x))
A
x’/sqrt(1-x^2)
20
Q
d/dx(arccos(x))
A
-x’/sqrt(1-x^2)
21
Q
d/dx(arctanx)
A
x’/1+x^2
22
Q
d/dx(arccot(x))
A
-x’/1+x^2
23
Q
d/dx(arcsec(x))
A
x’/abs(x)*sqrt(x^2-1)
24
Q
d/dx(arccsc(x))
A
x’/abs(x)*sqrt(x^2-1)
25
int(k*f(u)du)
k*int(f(u)du
26
int(f(x)+g(x)dx)
int(f(x)dx)+int(g(x)dx)
27
int(du)
u + C
28
int(du/u)
ln(abs(u)) + C
29
int(u^n)du
((u^(n+1))/n+1) + C
30
int(a^u(du))
((a^u)/ln(a))+C
31
int(sinu)du
-cos(u)+C
32
int(cos(u)du)
sinu + C
33
int(tan(u)du)
-ln(abs(cosu)) + C
34
int(cotu)(du)
ln(abs(sinu)) + C
35
int(sec(u)du)
ln(abs(secu + tanu)) + C
36
int(csc(u)du)
-ln(abs(cscu+cotu))+C
37
int(sec^2u du)
tanu + C
38
int(csc^2x)dx
-cotx+C
39
int(secutanudu)
secu + C
40
int(cscx+cotx)dx
-csc(x) + C
41
int(du/(sqrt(a^2 - u^2)))
arcsin(u/a) + C
42
int(du/(a^2+u^2))
(1/a) * arctan(u/a) + C
43
int(du/(u * sqrt(u^2 - a^2)))
(1/a)*arcsec(abs(u)/a) + C
