unit 2 Flashcards

1
Q

derivative of cosx

A

-sinx

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1
Q

derivative of sinx

A

cosx

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2
Q

derivative of tanx

A

sec^2x

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3
Q

derivative of cotx

A

-csc^2x

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4
Q

derivative of cscx

A

-cscxcotx

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4
Q

derivative of sec x

A

secxtanx

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5
Q

quotient rule derivative of u/v

A

v times derivative of u - u times derivative of v///////// v^2

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6
Q

product rule derivative of u times v

A

u times derivative of v + v times derivative of u

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7
Q

derivative of e^x

A

e^x

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8
Q

derivative of a^x

A

a^x times ln(a)

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9
Q

derivative of lnx

A

1/x

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10
Q

derivative of loga(x)

A

1/x times ln(a)

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11
Q

constant rule: derivative of c

A

0

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12
Q

constant multiple rule: derivative of c times u(a function) =

A

c times derivative of function

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13
Q

derivative of (u plus or minus v)

A

derivative of u plus or minus derivative of v

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14
Q

power rule: derivative of x^n

A

n times x^n-1

15
Q

differentiability implies….

A

continuity

16
Q

continuity does not imply….

A

differentiability

17
Q

the derivative fails to exist when the function has a….

A

-corner
-cusp
-vertical tangent

18
Q

a function cannot be differentiable if it is not…

A

continuous

19
Q

a function cannot be differentiable at a point if…

A

that point is not in its domain