Differentials Flashcards
When we write cos(𝑧) ′ as − sin(𝑧) 𝑧′, what rule causes
the 𝑧′ to appear?
Chain Rule
Why is 𝑥′ = 1 but 𝑧′ is not?
Because we assume “prime” means per x
If your problem talks about dollars per yen, what
variable has a derivative of 1?
yen = # of yen
If your problem talks about candies per box, what
variable has a derivative of 1?
box = # of boxes
What is (3y)′?
3y′
What do many students wrongly think (y)′ is?
yy’
Use ln(x) to “reduce”
(𝑥+3)^5 * (3𝑥−7)^8
______________
(2𝑥+8)^11
to simpler
operations.
5 ln(𝑥 + 3) + 8 ln(3𝑥 − 7) − 11 ln(2𝑥 + 8)
Translate into calc notation. The area is growing 5
square inches per second
𝐴′ = 5
Translate into calc notation. The side is shrinking 2
meters per second
𝑆′ = −2
What are the only “variables” you are allowed to plug in
values for before you take derivatives?
Constants
What’s the difference between dz and Δz?
dz is infinitely small but Δz is not
When are delta approximations most accurate?
When the deltas are small
Why do we use absolute values in experimental error?
Because we want the largest possible error. (We don’t want errors to cancel)
