Differentials Flashcards

1
Q

When we write cos(𝑧) ′ as − sin(𝑧) 𝑧′, what rule causes
the 𝑧′ to appear?

A

Chain Rule

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2
Q

Why is 𝑥′ = 1 but 𝑧′ is not?

A

Because we assume “prime” means per x

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3
Q

If your problem talks about dollars per yen, what
variable has a derivative of 1?

A

yen = # of yen

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4
Q

If your problem talks about candies per box, what
variable has a derivative of 1?

A

box = # of boxes

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5
Q

What is (3y)′?

A

3y′

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6
Q

What do many students wrongly think (y)′ is?

A

yy’

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7
Q

Use ln(x) to “reduce”

(𝑥+3)^5 * (3𝑥−7)^8
______________
(2𝑥+8)^11

to simpler
operations.

A

5 ln(𝑥 + 3) + 8 ln(3𝑥 − 7) − 11 ln(2𝑥 + 8)

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8
Q

Translate into calc notation. The area is growing 5
square inches per second

A

𝐴′ = 5

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9
Q

Translate into calc notation. The side is shrinking 2
meters per second

A

𝑆′ = −2

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10
Q

What are the only “variables” you are allowed to plug in
values for before you take derivatives?

A

Constants

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11
Q

What’s the difference between dz and Δz?

A

dz is infinitely small but Δz is not

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12
Q

When are delta approximations most accurate?

A

When the deltas are small

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13
Q

Why do we use absolute values in experimental error?

A

Because we want the largest possible error. (We don’t want errors to cancel)

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