derivatives Flashcards

1
Q

d/dx [cu]

A

cu’

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2
Q

d/dx [u ± v]

A

u’ ± v’

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3
Q

d/dx [uv]

A

uv’ + u’v

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4
Q

d/dx [u/v]

A

(vu’ - uv’) / v²

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5
Q

d/dx [c]

A

0

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6
Q

d/dx [uⁿ]

A

nuⁿ⁻¹ u’

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7
Q

d/dx [x]

A

1

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8
Q

d/dx [|u|]

A

(u / |u| ) (u’), u≠0

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9
Q

d/dx [ln u]

A

u’ / u

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10
Q

d/dx [eᵘ]

A

eᵘu’

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11
Q

d/dx [logₐ u]

A

u’ / ((ln a) u)

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12
Q

d/dx [aᵘ]

A

(ln a)aᵘu’

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13
Q

d/dx [sin u]

A

(cos u)u’

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14
Q

d/dx [cos u]

A

-(sin u)u’

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15
Q

d/dx [tan u]

A

(sec² u)u’

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16
Q

d/dx [cot u]

A

-(csc² u)u’

17
Q

d/dx [sec u]

A

(sec u tan u)u’

18
Q

d/dx [csc u]

A

-(csc u cot u)u’

19
Q

d/dx [arcsin u]

A

(u’ / √1-u²)

20
Q

d/dx [arccos u]

A

(-u’ / √1-u²)

21
Q

d/dx [arctan u]

A

(u’ / 1+u²)

22
Q

d/dx [arccot u]

A

(-u’ / 1+u²)

23
Q

d/dx [arcsec u]

A

(u’ / |u| √u²-1)

24
Q

d/dx [arccsc u]

A

(-u’ / |u| √u²-1)