Derivative Formulas Flashcards

1
Q

d/dx (c) =

A

0

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2
Q

d/dx [cf(x)] =

A

cf’(x)

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3
Q

d/dx (xn) =

A

nxn−1

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4
Q

d/dx [f(x) + g(x)] =

A

f’(x) + g’(x)

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5
Q

d/dx [f(x) − g(x)] =

A

f’(x) − g’(x)

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6
Q

d/dx [f(x)g(x)] =

A

f(x)g’(x) + g(x)f’(x)

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7
Q

d/dx [f(x)/g(x)] =

A

[g(x)f’(x) − f(x)g’(x)] / [g(x)]2

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8
Q

d/dx [f(g(x))] =

A

f’(g(x))g’(x)

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9
Q

d/dx (ln x) =

A

1/x

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10
Q

d/dx (logax) =

A

1/(x ln a)

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11
Q

d/dx (ex) =

A

ex

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12
Q

d/dx (ax) =

A

ax ln a

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13
Q

d/dx (sin x) =

A

cos x

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14
Q

d/dx (cos x) =

A

−sin x

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15
Q

d/dx (tan x) =

A

sec2x

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16
Q

d/dx (cot x) =

A

−csc2x

17
Q

d/dx (sec x) =

A

sec x tan x

18
Q

d/dx (csc x) =

A

−csc x cot x

19
Q

d/dx (sin−1x) =

A

1 / √(1−x2)

20
Q

d/dx (cos−1x) =

A

−1 / √(1−x2)

21
Q

d/dx (tan−1x) =

A

1 / (1+x2)

22
Q

d/dx (csc−1x) =

A

−1 / (|x|√(x2−1))

23
Q

d/dx (sec−1x) =

A

1 / (|x|√(x2−1))

24
Q

d/dx (cot−1x) =

A

−1 / (1+x2)