formula to know Flashcards
1
Q
Express logax in terms of logb
A
logbx/ logba
2
Q
sinh 2x
A
2*sinh(x)*cosh(x)
3
Q
cosh(2x)
A
cosh2(x) + sinh2(x)
4
Q
quotient rule
A
y=u/v
(v*u’-u*v’)/v2
5
Q
intergration by parts
A
∫u*v’=u*v-∫v*u’
6
Q
diff of tan kx
A
ksec2 kx
7
Q
diff of sec x
A
sec x * tan x
8
Q
diff of cot x
A
-cosec2x
9
Q
diff of cosec x
A
-cosec x * cot x
10
Q
diff of arcsin x
A
1/ (1-x2)0.5
11
Q
diff of arc cos(x)
A
-1/ (1-x2)0.5
12
Q
diff of arctan(x)
A
1 / 1+x2
13
Q
diff of tanh(x)
A
sech2(x)
14
Q
diff of arsinh(x)
A
1 / (1+x2)0.5
15
Q
diff of arcosh (x)
A
1 / (x2-1)0.5
16
Q
diff of artanh(x)
A
1 / (1-x2)
17
Q
∫sec2 kx
A
(1/k) tan(kx)
18
Q
∫tan x
A
ln |sec x|
19
Q
∫ cot(x)
A
ln |sin x|
20
Q
∫tanh x
A
ln (coshx)
21
Q
What links together cosh and sinh?
A
cosh2-sinh2=1
22
Q
What is sinh(2x) equal to?
A
2*sinh(x)*cosh(x)
23
Q
cosh(2x)=
A
sinh2(x)+cosh2(x)
24
Q
logaX=
A
logbX/logba
25
ksec2 kx
diff of tan kx
26
sec x \* tan x
diff of sec x
27
-cosec2x
diff of cot x
28
-cosec x \* cot x
diff of cosec x
29
1/ (1-x2)0.5
diff of arcsin x
30
-1/ (1-x2)0.5
diff of arc cos(x)
31
1 / 1+x2
diff of arctan(x)
32
sech2(x)
diff of tanh(x)
33
1 / (1+x2)0.5
diff of arsinh(x)
34
1 / (x2-1)0.5
diff of arcosh (x)
35
1 / (1-x2)
diff of artanh(x)
36
arcsin(x)=
-arcsin(-x)
37
arcos(x)
π-arcos(-x)
38
arctan(x)
-arctan(-x)
39
what is root i?
1/√2 + 1/√2i
40
