DERIVATIVES/ANTIDERIVATIVES Flashcards

1
Q

antiderivative of a/x

A

a ln |x|

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2
Q

antiderivative of sin x

A

-cos x

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3
Q

antiderivative of cos x

A

sin x

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4
Q

antiderivative of tan x

A

ln |sec x|

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5
Q

antiderivative of sec x

A

ln |sec x + tan x|

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6
Q

antiderivative of csc x

A

(-) ln |cot x + csc x| *check this one

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7
Q

antiderivative of csc^2 x

A

-cot x

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8
Q

antiderivative of ln x

A

xlnx-x

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9
Q

antiderivative of e^x

A

e^x

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10
Q

derivative of e^x

A

e^x

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11
Q

derivative of ln x

A

1/x

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12
Q

derivative of tan x

A

sec ^2 x

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13
Q

derivative of csc x

A

-csc x * cot x

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14
Q

derivative of sec x

A

sec x tan x

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15
Q

derivative of cot x

A

-csc^2 x

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16
Q

derivative of b^x

A

b^x * lnb

17
Q

derivative of log b(subscript) x

A

1/xlnb

18
Q

derivative of arctan x

A

1/ (1+x^2)

19
Q

derivative of arccos x

A

-1/sqrt(1-x^2)

20
Q

derivative of arcsin x

A

1/sqrt(1-x^2)

21
Q

antiderivative of 1/ (1+x^2)

A

arctan x

22
Q

antiderivative of -1/sqrt(1-x^2)

A

arccos x

23
Q

antiderivative of 1/sqrt(1-x^2)

A

arcsin x

24
Q

antiderivative of sec x tan x

A

sec x

25
Q

antiderivative of sec ^2 x

A

tan x