Question

implicit differentiation 2x^2+7 x y-y^2=8

Answer 1

take the derivative of 2x^2 using power rule and let me know what you get

Answer 2

4x

Answer 3

very well. lets move to the next term. 7xy

Answer 4

7x dy/dx + y?

Answer 5

ok so 7 here is a constant. so you can for now just leave it out for now.
focus on xy. the derivative of xy is (1)(y)+(x)(1)(y') ; y' can also be written as dy/dx

Answer 6

then you multiply 7 with the derivative so it becomes 7(y+x dy/dx) or 7(y+xy')

Answer 7

so then can I also say 7x dy/dx + 7y ?

Answer 8

yes you can

Answer 9

so far I had -4x-7y/(7x-2y) when I did it myself but answer is showwing wrong.

Answer 10

apparently my signs are all wrong, not sure where I went wrong

Answer 11

lets move on. take derivative of -y^2

Answer 12

ok... uh -2y dy/dx ?

Answer 13

yup that's right

Answer 14

and finally derivative of 8 = 0

Answer 15

so we have 4x+7x dydx + 7y - 2y dydx=0

Answer 16

yes

Answer 17

so up till now is there any thing that you don't understand ?

Answer 18

Okay then we do 7x dydx - 2y dydx = -4x-7y

Answer 19

then we get -4x-7y/ (7x-2y)

Answer 20

correcct?

Answer 21

but the answer says the signs are suppose to be the opposite

Answer 22

hmmm. that is really interesting. let me double check

Answer 23

ohhh

Answer 24

?

Answer 25

our answer is right. your grading system multiplied everything my -1, to get rid of the -1 from the numerator ( top part of fraction)

Answer 26

ohhhhhhhhhhh am I always suppose to do that| ?

Answer 27

well, if you are giving a test on paper then you don't have to do that but since the grading system is built this way i guess you have to do it, yeah. ( i personally think it is pretty stupid)

Answer 28

oh okay thanks ! so if its xy right, just put dydx beisde the x?

Answer 29

in implicit differentiation you are differentiation y twice. the first time you differentiate it like normal. so for example if it xy^2 ==> (1)(y^2)+(x)(2y)(dy/dx)

Answer 30

then after you differentiate it normally you add dy/dx on the y not the x

Answer 31

so you are differentiating y twice in a way

Answer 32

for practice try solving this one --> 2xy = xy^3 = 9

Answer 33

okay so, 2x dydx + 2y = 3x^2 dydx + 3 y^2 = 0 ?

Answer 34

let me see

Answer 35

it was suppose to be a plus sign not equal sign. my mistake over there. the first = sign is a + sign

Answer 36

oh okay, 2xy + xy^3 = 9, 2x dydx +y + 3x^2 dydx + 3y^2 = 0 ?