Derivative Rules Flashcards

1
Q

Quotient Rule Phrase

A

low d high minus high d low, square the bottom and off we go

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2
Q

f(x)= mx^(n)

A

f’(x)= mnx^(n-1)

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3
Q

Derivative Notation

A

f’(x) y’ (dy)/(dx) (df(x))/(dx) d/(dx)

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4
Q

Product rule

A

f’(x)= f’g + g’f

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5
Q

Quotient rule

A

(gf’ -fg’)/g²

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6
Q

Differentiability

A

Must be continuous at x=c and left-hand derivative= right-hand derivative

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7
Q

Derivative definition

A

Slope of the tangent line at a point

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8
Q

f(g(x))

A

f’(g(x)) × g’(x)

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9
Q

Average rate of change

A

2 places (Δy/Δx)

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10
Q

Instantaneous Rate of Change

A

Derivative of function

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11
Q

Matching Graphs of Functions

A

if graph 1 is f(x), then graph 2 of f’(x) will have x-intercepts at all relative extrema (max’s and min’s)

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12
Q

Piecewise Functions (both differentiable and continuous)

A
  1. Plug in x-values and set original equations equal too each other
  2. Take derivatives of equations and set equal to each other (then plug in x-value)
  3. Set up a system of equations
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13
Q

Piecewise Functions (just continuous)

A
  1. Plug in x-values and set equations equal to each other (repeat if more than 2 equations)
  2. Set up a system of equations
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14
Q

Find points where horizontal or vertical tangent line

A

f’(x) = a/ b
1. Horizontal is set a = 0
2. Vertical is set b = 0

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15
Q

Average ROC

A

slope of secant line

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