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Calculus (AB) - Derivatives, AntiDerivatives and Theorems Flashcards | StudBud
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Calculus (AB) - Derivatives, AntiDerivatives and Theorems
d/dx [csc u] =
integral of eudu =
Calculus (AB) - Derivatives, AntiDerivatives and Theorems
29 terms
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Answers
1
integral of e
u
du
=
e^u + C
-ln|cos u| + C
ln|sec(u) + tan(u)| + C
ln|sin u| + C
2
d/dx [csc u] =
-csc(u)cot(u) * (u')
sec^2(u) * (u')
sec(u)tan(u) * (u')
-csc^2(u) * (u')
3
integral of sec
udu
=
-ln|cos u| + C
ln|csc(u) + cot(u)| + C
ln|sin u| + C
ln|sec(u) + tan(u)| + C
4
integral of cot
udu
=
ln|sec(u) + tan(u)| + C
a^u/ln(a) + C
-ln|cos u| + C
ln|sin u| + C
5
integral of sec(
u
)tan(
u
)
udu
=
tan(u) + C
-cot(u) + C
sec(u) + C
-csc(u) + C
6
d/dx [cos u] =
-sin(u) * (u')
sec(u) * (u')
-csc^2(u) * (u')
-cos(u) * (u')
7
d/dx [log
a
u] =
u'/u ln(a)
a^u * u' * ln(a)
u'/(u) * ln(a)
u'/square root of 1-u^2
8
integral of csc
2
udu
=
tan(u) + C
-cot(u) + C
-csc(u) + C
-sin(u) + C
9
d/dx [tan u] =
sec^2(u) * (u')
-sin(u) * (u')
sec(u)tan(u) * (u')
cos(u) * (u')
10
integral of sec
2
udu
=
-sin(u) + C
-cot(u) + C
tan(u) + C
-csc(u) + C
11
d/dx [sin u] =
-csc^2(u) * (u')
cos(u) * (u')
-csc(u)cot(u) * (u')
-sin(u) * (u')
12
d/dx [e
u
] =
e^u * u'
u'/(u) * ln(a)
a^u * u' * ln(a)
u'/u or 1/u * u'
13
d/dx [sec u] =
-csc^2(u) * (u')
cos(u) * (u')
sec^2(u) * (u')
sec(u)tan(u) * (u')
14
Fundamental Theorem of Calculus - Derivative part =
d/x [integral (c,x) of f(t)dt] = f(x)
d/dx [integral (c,u) of f(t)dt] = f(u) * (u')
integral (a,b) of f(x)dx = F(b) - F(a)
its not this one
15
integral of tan
udu
=
-ln|cos u| + C
ln|sec(u) + tan(u)| + C
a^u/ln(a) + C
ln|u| + C
16
d/dx [tan x] =
sec(x)tan(x)
-csc^2x
cot(x)
sec^2x
17
integral of csc(
u
)cot(
u
)
udu
=
tan(u) + C
-cot(u) + C
sec(u) + C
-csc(u) + C
18
d/dx [a
u
] =
u'/u or 1/u * u'
u'/(u) * ln(a)
e^u * u'
a^u * u' * ln(a)
19
integral of cos
udu
=
-sin(u) + C
-cos(u) + C
tan(u) + C
sin(u) + C
20
d/dx [ln u] =
a^u * u' * ln(a)
u'/u or 1/u * u'
u'/(u) * ln(a)
u'/square root of 1-u^2
21
Fundamental Theorem of Calculus - Evaluation part =
its not this one
d/x [integral (c,x) of f(t)dt] = f(x)
integral (a,b) of f(x)dx = F(b) - F(a)
d/dx [integral (c,u) of f(t)dt] = f(u) * (u')
22
integral of csc
udu
=
-ln|cos u| + C
-ln|csc(u) + cot(u)| + C
ln|sin u| + C
ln|sec(u) + tan(u)| + C
23
d/dx [cot u] =
sec^2(u) * (u')
-csc^2(u) * (u')
cos(u) * (u')
sec(u)tan(u) * (u')
24
integral of a
u
du
=
a^u/ln(a) + C
e^u + C
ln|sin u| + C
-ln|cos u| + C
25
integral of sin
udu
=
-cos(u) + C
-sin(u) + C
tan(u) + C
cos(u) + C
26
d/dx [csc x] =
-csc(x)cot(x)
sec(x)tan(x)
sec(x)tan(x)
sec^2x
27
integral of
du
/
u
=
ln|sin u| + C
ln|cos u| + C
ln|u| + C
a^u/ln(a) + C
28
d/dx [cot x] =
-csc^2x
sec(x)tan(x)
-csc(x)cot(x)
sec^2x
29
d/dx [sec x] =
-csc^2x
-csc(x)cot(x)
sec(x)tan(x)
sec^2x
