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Calculus Formulas for AP
Calculus Formulas for AP
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AP Calculus Formulas to Know & Understand
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Questions
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1
Find the derivative:
1/(xlna)
1/(lna)
ax∙lna
x/(lna)
2
Complete:
concave up
POSSIBLE maximum or minimum
GUARANTEED maximum or minimum
concave down
3
Complete:
horizontal asymptotoe
hole
vertical asymptote
0
4
Integrate:
-sinu + C
cosu + C
sinu + C
-cosu + C
5
Integrate:
ln|cscu+cotu| + C
-ln|secu+tanu| + C
ln|secu+tanu| + C
-ln|cscu+cotu| + C
6
Find the derivative:
-u'/[|u|√(u2+1)]
u'/[|u|√(u2-1)]
-u'/[|u|√(u2-1)]
u'/[|u|√(u2+1)]
7
Find the derivative:
-u'/√(1-u2)
-u'/(1+u2)
-u'/(1-u2)
-u'/√(1+u2)
8
Integrate:
1/lna + C
lna/au + C
au + C
au/lna + C
9
Integrate:
xn+1/n + C
nxn-1 + C
xn/(n+1) + C
xn+1/(n+1) + C
10
Find the derivative:
nxn
nxn-1
(n-1)xn-1
nx
11
Find the derivative:
u'v+uv'
u'v-uv'
u'+v'
(uv)n-1
12
Find the derivative:
-sec2x
-csc2x
-cscxcotx
secx
13
Integrate:
eu + C
ln|u| + C
lnu + C
u-1 + C
14
The following formulas are used to represent the _________________.
average acceleration
average rate of change or average velocity
change in position
average time
15
Integrate:
-cosu + C
-sinu + C
cosu + C
cos2x + C
16
Find the derivative:
1/(lnx)
x'∙lnx
(lnx)/x
1/x
17
Integrate:
(1/a)arcsec(|u|/a) + C
(1/a)arctan(u/a) + C
arcsin(u/a) + C
arctan(u/a) + C
18
Find the derivative:
sin2x
-cscxcosx
-sinx
sinx
19
Integrate:
(1/a)arcsec(|u|/a) + C
arcsin(u/a) + C
(1/a)arctan(u/a) + C
arctan(u/a) + C
20
Find the derivative:
-sec2x
-cscxcotx
-cosx
-csc2x
21
Integrate:
-ln|secu+tanu| + C
ln|cscu+cotu| + C
-ln|cscu+cotu| + C
ln|secu+tanu| + C
22
Find the derivative:
ex-1
(x-1)ex
xex-1
ex
23
Find the derivative:
csc2x
sinx/cosx
sec2x
secx
24
Find the derivative:
u'v+uv'
(u'v+v'u)/(v2)
(u'v-v'u)/(v2)
u'v-uv'
25
Find the derivative:
-cosx
cos2x
cosx
-sinx
26
Complete:
GUARANTEED maximum or minimum
GUARANTEED Point of Inflection
POSSIBLE Point of Inflection
POSSIBLE maximum or minimum
27
Find the derivative:
-u'/[|u|√(u2+1)]
-u'/[|u|√(u2-1)]
u'/[|u|√(u2-1)]
u'/[|u|√(u2+1)]
28
Find the derivative:
-u'/√(1-u2)
u'/(1+u2)
-u'/(1+u2)
-u'/√(1+u2)
29
Integrate:
(1/a)arcsec(|u|/a) + C
arctan(u/a) + C
(1/a)arctan(u/a) + C
arcsec(u/a) + C
30
The following formula is used to represent the _________________.
maximum velocity
displacement
average value
total distance traveled
31
Integrate:
2secu + C
cotu + C
2secutanu + C
tanu + C
32
Integrate:
tanu + C
secu + C
-cscu + C
cscu + C
33
Complete:
hole
vertical asymptote
horizontal asymptotoe
0
34
Integrate:
eu/(u+1) + C
ueu-1 + C
eu/u + C
eu + C
35
Complete:
concavity
minimum
slope
maximum
36
Integrate:
tanu + C
cscu + C
-cscu + C
secu + C
37
Integrate:
ln|cosu| + C
ln|sinu| + C
-ln|cosu| + C
-ln|sinu| + C
38
Integrate:
ln|cosu| + C
-ln|sinu| + C
-ln|cosu| + C
ln|sinu| + C
39
Complete:
maximum
minimum
concavity
slope
40
Complete:
velocity
|velocity|
|position|
position
41
Find the derivative:
tan2x
secxtanx
cscxtanx
sec2x
42
Find the derivative:
u'/√(1-u2)
u'/√(1+u2)
u'/(1+u2)
-u'/(1+u2)
43
Find the derivative:
x∙ax-1
ax-1
ax
ax∙lna
44
Find the derivative:
f'(g'(x))
f'(g(x))∙g'(x)
f(g'(x))
f'(g(x))
45
Find the derivative:
1/[f'(f-1(a))]
1/[f'(a)]
f'(a)
1/[f-1(f'(a))]
46
Find the derivative:
-u'/√(1-u2)
u'/(1+u2)
-u'/(1+u2)
u'/√(1-u2)
47
Integrate:
tanu + C
cotu + C
-cotu + C
-tanu + C
