Can anyone help me on this incredibly long problem? ;_;
http://i.imgur.com/bCV0P1R.jpg
# 36
I swear to god I spend too much time on it and I still haven't gotten an answer. :\ Is there anyway to find the answer in a shorter way?

Question

Can anyone help me on this incredibly long problem? ;_; 
http://i.imgur.com/bCV0P1R.jpg
# 36
I swear to god I spend too much time on it and I still haven't gotten an answer. :\ Is there anyway to find the answer in a shorter way?

anonymous · Answer

Hope this helps

anonymous · Answer

omg that looks so beautifully short!! i was wondering if u could post up a better quality pic tho... >< sry if im asking for too much but i cant really see it :<

anonymous · Answer

Hopefully this is a little better. You can ask about any parts you can't see

anonymous · Answer

correct me if im wrong but is this what u did? 1) find the derivative of the whole equation 2.) u simplified it to 2x2yy' = 2 but then... i cant tell what the symbol on the left is on the next line. is it y'?

anonymous · Answer

yes

anonymous · Answer

y'(2x2y)=2 
y'=2/(2x2y) Which is 1/(xy)

anonymous · Answer

then you find the derivative of 1/(xy)

anonymous · Answer

to find the derivative of 1/(xy) you have to use the quotient rule.

anonymous · Answer

wait how is y' = 2/(2x2y) = 1/(xy). isn't it 1/(2xy)?

anonymous · Answer

the 2s cancel because they are being multiplied

anonymous · Answer

does just one 2 cancel?

anonymous · Answer

doesnt*

anonymous · Answer

no because if you factor out a two on the bottom you are left with xy not 2xy

anonymous · Answer

(2*x*2*y) = (4*x*y) im sure of that tho...

anonymous · Answer

and wait a minute... ur first step is wrong too... ur suppose to use the product rule to find the derivative of x^(2)y^(2)

anonymous · Answer

i knew that was too short to be true. im sorry but im just really frustrated of this problem. its so long...

anonymous · Answer

You're right, I made a mistake on the first step.

ganeshie8 · Answer

$\large x^2y^2 - 2x = 3 $

implicit diff both sides

$\large x^2 (2yy') + y^2(2x) - 2 = 0 $

solve y'

$\large y' = \frac{1-xy^2}{x^2y} $

ganeshie8 · Answer

quotient rule and find y''

anonymous · Answer

okay. ty. :'<

ganeshie8 · Answer

np :) u wil have to plug product rule again, but if you're careful ,u wil end wid something simple

ganeshie8 · Answer

or simplify a bit before taking second deriv

$\large y' = \frac{1-xy^2}{x^2y} $

$\large y'  = \frac{1}{x^2y} - \frac{y}{x} $

$\large y^{'}  = x^{-2} y^{-1} - yx^{-1}$