Derivatives 2 Memorize. Flashcards

1
Q

f(x) = sinx

A

f¹(x) = cosx

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2
Q

f(x)= cosx

A

f¹(x) = -sinx

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3
Q

f(x) = tanx

A

f¹(x) = sec²x

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4
Q

f(x) = cotx

A

f¹(x) = -csc²x

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5
Q

f(x) = secx

A

f¹(x) = secxtanx

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6
Q

f(x) = cscx

A

f¹(x) = -cscxcotx

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7
Q

f(x) = sin⁻¹x

A

f¹(x) = 1/ sqrt (1-x²)

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8
Q

f(x) = cos⁻¹x

A

f¹(x) = -1/sqrt (1-x²)

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9
Q

f(x) = tan⁻¹x

A

f¹(x) = 1/ 1+x²

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10
Q

f(x) = cot⁻¹x

A

f¹(x) = -1/ 1+x²

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11
Q

f(x) = sec⁻¹x

A

f¹(x) = 1/ |x| (sqrt x² -1)

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12
Q

f(x) =csc⁻¹x

A

f¹(x) = -1/ |x| (sqrt x² -1)

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13
Q

f(x) = eˣ

A

f¹(x) = eˣ

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14
Q

f(x) = 2ˣ

A

f¹(x) = 2ˣ ln2

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15
Q

f(x) = lnx

A

f¹(x) = 1/x

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16
Q

f(x) = log₅x

A

f¹(x) = 1/ xln5

17
Q

f(x) = -6

A

f¹(x) = 0

18
Q

f(x) = 8x

A

f¹(x) = 8

19
Q

f(x) = x²

A

f¹(x) = 2x

20
Q

f(x) = x⁻³ or f(x) = 1/x³

A

f¹(x) = -3/x⁴

21
Q

f(x) = sqrt x

A

f¹(x) = 1/ 2 sqrtx

22
Q

f(x) = x¹/⁵

A

f¹(x) = 1/5 x⁻⁴/⁵