Question

this is an implicit differentiation...
(xy)^1/2=x+3y Please help :)

Answer 1

( √u ) ' = ...?
u = xy --> u' = ....?

Answer 2

@lizlozada How much you can fill in?

Answer 3

ummm 1/2(xy)^-1/2(xy'+y)+1+3y'

Answer 4

*=1+3y

Answer 5

I want you to fill in what I'm asking!

Answer 6

sorry that's the best i can do because we didn't learn with u, we learned like that

Answer 7

what u have written is correct!
do u need to isolate y' ?

Answer 8

yes

Answer 9

thats my struggle

Answer 10

let me give u hint
from the question : (xy)^(1/2) = x+3y
so
(xy)^(-1/2) = 1/ (xy)^(1/2) = ?

Answer 11

and right side is 1+3y'

Answer 12

what happened to the 1/2 in front of (xy)^(-1/2)

Answer 13

it will be there,
1/2 (xy)^(-1/2) = 1/2 (xy)^(1/2) = ?
do u need to prove y' = something, or just find y'

Answer 14

just find it

Answer 15

then forget that hint.
just distribute
[1/2(xy)^-1/2](xy'+y)=1+3y'
xy' [1/2(xy)^-1/2] + y [1/2(xy)^-1/2] = 1+3y'
now collect y' terms on one side

Answer 16

got that ?
i just distributed [1/2(xy)^-1/2]

Answer 17

distributed into what?