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calculus > derivatives > Flashcards

derivatives Flashcards

1
Q

derivative of position

A

velocity

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2
Q

derivative of velocity

A

acceleration

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3
Q

what is instantaneous velocity

A

s’(t)

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4
Q

what is average velocity

A

distance/ time

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5
Q

how do you know when the particle is speeding up or slowing down

A

it is speeding up when v(t) and a(t) have the same sign. it is slowing down when they have opposite signs

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6
Q

when is the particle moving from left to right

A

when v(t)>0

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7
Q

when is the particle moving from right to left

A

when v(t)<0

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8
Q

what is the derivative of sinx

A

cosx

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9
Q

what is the derivative of cosx

A

-sinx

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10
Q

what is the derivative of tanx

A

sec^2x

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11
Q

what is the derivative of cotx

A

-csc^2x

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12
Q

what is the derivative of secx

A

secxtanx

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13
Q

what is the derivative of cscx

A

-cscxcotx

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14
Q

chain rule

A

derivative of outer x derivative of inner

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15
Q

product rule

A

(first)(derivative of second)+(second)(derivative of first)

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16
Q

quotient rule

A

((bottom)(derivative of top)-(top)(derivative of bottom))/(bottom)^2

17
Q

inverse function theorem

A

(f^-1)’ = 1/ f’(f^-1(x))

18
Q

derivative of inverse sin x

A

1/ √(1-x^2)

18
Q

derivative of inverse cos x

A

-1/ √(1-x^2)

19
Q

derivative of inverse tan x

A

1/ (1+x^2)

20
Q

derivative of inverse cot x

A

-1/ (1+x^2)

21
Q

derivative of inverse sec x

A

1/ lxl√(x^2-1)

22
Q

derivative of inverse csc x

A

-1/ lxl√(x^2-1)

23
Q

implicit differentiation steps

A
  1. derivative of both sides
  2. move all of the y’ to one side
  3. solve for y’
  4. if applicable, plug in the given
24
Q

lnx=

A

logeX

25
Q

logx

A

log10X

26
Q

derivative of e^x

A

e^x

27
Q

derivative of lnx

A

1/x

28
Q

derivative of b^x

A

B^xlnb

29
Q

derivative of logbX

A

1/(xlnb)

30
Q

derivative of e^u

A

e^u*u’

31
Q

derivative of b^u

A

b^u*u’lnb

32
Q

derivative of lnu

A

u’/u

33
Q
A

calculus (1 decks)

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