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

Question

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

anonymous · Answer

( √u ) ' = ...?
    u     = xy    --> u' = ....?

anonymous · Answer

@lizlozada How much you can fill in?

anonymous · Answer

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

anonymous · Answer

*=1+3y

anonymous · Answer

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

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

yes

anonymous · Answer

thats my struggle

hartnn · Answer

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

hartnn · Answer

and right side is 1+3y'

anonymous · Answer

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

hartnn · Answer

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'

anonymous · Answer

just find it

hartnn · Answer

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

hartnn · Answer

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

anonymous · Answer

distributed into what?

hartnn · Answer

|dw:1350363357671:dw|

hartnn · Answer

|dw:1350363493382:dw|