Question

calculus help 10 questions

Answer 1

about to post give me a sec!

Answer 2

@mhchen

Answer 3

@Tranquility

Answer 4

number 6 requires work

Answer 5

@nuts

Answer 6

@Tranquility

Answer 7

@Vocaloid

Answer 8

for 1 just apply the product rule to the derivative and fill in the derivative for csc^-1

Answer 9

for 2, identify the parts where the derivative would be 0 (where the slope of the original function is 0), where the derivative is positive (where the original function is increasing) and where the derivative is negative (where the original function is decreasing) and piece together the derivative

Answer 10

for 3, just take the derivative wrt x two times

Answer 11

is 1 D?

Answer 12

for 4 just take the derivative, plug in x = 2 and round

Answer 13

yeah that's what i got too

Answer 14

2 is a or d

Answer 15

check again

remember the derivative must be positive at both extremes

Answer 16

I meant a or e

Answer 17

sorry

Answer 18

3 is false because it is 3/2 not 5/2

Answer 19

there are only two choices (b and d) where the derivative is positive at both extremes of the graph

between b and d see which one has the derivative end behavior that matches the behavior of the graph
notice how the original graph is increasing at either extreme and only decreasing in the middle

Answer 20

c looks like it since you plot points where it is 0

Answer 21

second derivative, not the first derivative

Answer 22

3*x^(1/2)

first derivative = 3 * (-1/2) * x^(-3/2)

second derivative = 3 * (1/2) * (-3/2) * x^(-5/2) = 9/(4x^(5/2))

Answer 23

okay that makes sense

Answer 24

so 4 take derivative and then plug 2 in right ?

Answer 25

yes

Answer 26

f'(2)=-7/8

Answer 27

good

they want a decimal to two places so -0.88

Answer 28

yep

Answer 29

same logic as before just take the derivative and plug in x = 4

Answer 30

sneaky... \(\frac{d}{dx}\sin(\ln(-8x^2))\)

Answer 31

that's what I thought

Answer 32

is the sin question correct?

Answer 33

i think so

Answer 34

\(-8x^2\leq0\)

therefore \(\ln(-8x^2)\) is undefined

Answer 35

I'm betting they didn't take that into account when making the question though

Answer 36

if you allow negative values into the log function then you have to introduce branch cuts

Answer 37

okay so for this sake idk if it's true or false but let me work on the easier ones

Answer 38

-2976

Answer 39

@Vocaloid

Answer 40

yeah that's it

Answer 41

I am working on some others and you can check them

Answer 42

@Vocaloid

Answer 43

good

Answer 44

do I do 2nd derivative here?

Answer 45

@Vocaloid

Answer 46

last few questions

Answer 47

yes you would take the implicit second derivative

Answer 48

so take 2nd and then plug in?

Answer 49

yes

Answer 50

I messed up someone could you help me

Answer 51

is 1 of the last 2 correct

Answer 52

@Vocaloid

Answer 53

yes

Answer 54

okay so the second derivative question I messed up

Answer 55

take the first implicit derivative

then solve for the dy/dx term by moving all the variables to one side

then take the derivative again

Answer 56

this is what I got

Answer 57

but I have no y to plug in

Answer 58

where are you getting c from

Answer 59

the whole dx du formula thing c is constant or something

Answer 60

let's just start over

Answer 61

okay I think I have it now

Answer 62

1/3 or.33

Answer 63

@Vocaloid

Answer 64

one more question above and then 'm done I promise

Answer 65

basically the formula they give you allows you to calculate the slope of the line at x = 9 at infinitely small intervals between 9 and h, giving you the slope of the tangent, and thus, the derivative

Answer 66

what about secnt line

Answer 67

i don't think it's relevant here

Answer 68

okay yay thank yo uso much!