Calc identities Flashcards

1
Q

f ‘(sin x) = ?

A

cos x

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2
Q

f ‘ (cos x) = ?

A
  • sin x
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3
Q

f ‘(tan x) = ?

A

sec^2 x

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4
Q

f ‘(sec x) = ?

A

sec x tan x

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5
Q

f ‘(cot x) = ?

A

-csc^2 x

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6
Q

f ‘(csc x) = ?

A
  • csc x cot x
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7
Q

power rule

A

f ‘(x^n) = n x^(n-1)

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8
Q

constant multiple rule

A

f ‘[c f(x)] = c f ‘[f (x)]

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9
Q

chain rule

A

dy/dx = (dy / du) (du / dx) d/dx [f(g(x))] = f ‘[g(x)] g ‘(x) d/dx [f(u)] = f ‘(u) du/dx

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10
Q

What is the derivative of arcsine?

A
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11
Q

What is the derivative of arccosine?

A
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12
Q

What is the derivative of arctangent?

A
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13
Q

What is the derivative of arccotangent?

A
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14
Q

What is the derivative of arcsecant?

A
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15
Q

What is ther derivative of arccosecant?

A
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16
Q

What is the derivative of e^x?

A

e^x * x’

17
Q

What is the derivative of b^x when b is a constant?

A

b^x * ln(b) * x’

18
Q

What is the derivative of ln(x)?

A

1/x * x’

19
Q

What is the derivative of log b (u)

A

1/(x * ln b) * dx