Question

Can somone please look at this question

Answer 1

@amistre64 can you please help me with this problem please

Answer 2

your going to simply have to take the derivative ...

Answer 3

we can move the x parts to one side if that helps

Answer 4

ok

Answer 5

\[y^2 -6y = 4+4x-x^2\]
at least this want its primed for y'

Answer 6

ok I am having a little trouble doing the deriviative

Answer 7

do you know the power rule and constant rule?

Answer 8

yes

Answer 9

then your confusion is most likely due to thinking that x and y have some special supermathical properties other than jsut being redundant names for generality

Answer 10

spose i give you w^3, what does your gut say is the derivative?

Answer 11

3

Answer 12

you know the power rule

Answer 13

sorry I am just learning calculus and I have bad teacher so I am most likey not going to understand some things we are just learning the power rule

Answer 14

drop the power in front and take away 1

w^3 -> 3w^2 whould be your gut feeling, but theres a catch

Answer 15

ok

Answer 16

without knowing what the derivative is "with respect to"; the variable pops out a prime:

w^3 -> 3w^2 w'

Answer 17

ok so then for my problem is it 2x+2y-4x-6y=4 and then combine

Answer 18

thats a good start, but lets pop out those primes, and remember that a constant goes to 0

x^2 + y^2 - 4x -6y = 4

2x x' + 2y y' - 4 x' - 6 y' = 0

Answer 19

oh ok

Answer 20

now that we have it in this setup, lets define this for "with respect to x", which means that x'=1

2x + 2y y' - 4 - 6 y' = 0

now algebra this to "solve" for y'

Answer 21

ok

Answer 22

so for the x I put in 1 what do I do with the y's

Answer 23

for the x' we put in 1, which the simplifes this to what i wrote

2x + 2y y' - 4 - 6 y' = 0

we want to move this around so that y' is on the left and the rest of it is in the right

we are NOT inputing any specific values for x or y, we are just creating an equation that would allow us to determine y' for any given (x,y) in f(x,y)

Answer 24

ok

Answer 25

4-2x=2y y'-6y'

Answer 26

good so far, know factor out (undistribute) that y'; and divide off the excess

Answer 27

we can factor our a 2 as well from it all to reduce those coefficients

Answer 28

I am confussed can you walk me through this

Answer 29

the distributive property from algebra classes is:

a(p+q) = ap + aq , when a sum of parts has a like factor, we can "undistribute it" or factor it out

ap + aq = a(p+q)

Answer 30

since all your terms on the right side have a y' as a factor, pull it out

Answer 31

y(2-6)

Answer 32

4 - 2x = 2y y' - 6y'

4 - 2x = (2y - 6) y'

Answer 33

now whats left in order to get y' all by its little lonesome?

Answer 34

take everything so it looks likey'= (4-2x/2y-6)

Answer 35

thats looking better yes

we can simplify that by dividing the top and bottom by 2\[y'=\frac{4-2x}{2y-6}\]
\[y'=\frac{2-x}{y-3}\]

Answer 36

ok I am following

Answer 37

thats it; y' is a simpler notation than dy/dx, but they mean the same thing

Answer 38

oh ok I am following yah now this way is way easier than what my techer was trying to teach us

Answer 39

i know :)

Answer 40

ok thanks

Answer 41

good luck