Basic calc I problem: calculate y''

[94JZA80]

This is a simple calc I problem that I'm having trouble solving (most likely b/c I'm making an extremely stupid/simple mistake somewhere).

Homework Statement

Given the equation x² +6xy + y² = 8, calculate y''

The answer, according to the text, is y'' = 64/(3x + y)³. However, if you inspect my work below, you'll see that I'm having some trouble arriving at this solution. I've already gone through my work a few times and corrected some silly algebraic errors and omissions. But as you can see, my work still has some errors that I'm unable to find b/c my solution contains a numerator that is more complex than the simple constant "64" that it should be. Specifically, some terms in the numerator aren't completely canceling out, leaving a "-8x" term and a "-2" term in the polynomial that is the numerator...and i don't know if the error is in my algebra or my implicit differentiation. That being said, i can see already that if those specific terms weren't there, the numerator would then be 64(x² +6xy + y²), which equals 64(8). This "8" in the numerator would then cancel with the "8" in the denominator 8(3x + y)³, leaving the correct answer of y'' = 64/(3x + y)³. again, i don't know if the things that should be canceling out aren't canceling out b/c of an algebra error or a differentiation error. Any help would be appreciated very much.

Homework Equations

see section 3 below...

The Attempt at a Solution

[PLAIN]http://img801.imageshack.us/img801/1048/scanmed.jpg


...if anyone has questions about what they're looking at, just ask me and i will do my best to elaborate on how i got from one particular step to the next. Also, to the moderators, i am new and this is my first post. i did read the rules at the top of the sub-forum and did my best to follow the requested format. if something doesn't appear legit in my thread, please contact me before deleting it entirely without reason or notice.

TIA,
Eric

 

[CompuChip]

I didn't go through all of it, but despite your best effort I found a little mistake on the first line (sorry!)
What is the derivative of 8?

 

[94JZA80]

I didn't go through all of it, but despite your best effort I found a little mistake on the first line (sorry!)
What is the derivative of 8?

OMG ...like i suspected, it was probably something really simple and stupid. i feel like a dummy now LOL. thanks for the catch though! i probably would have kept overlooking that error on the assumption that i couldn't have possibly calculated the first derivative incorrectly LOL...i guess i was wrong!

i'm at work now, so i won't get a chance to rework the problem until this evening. but as soon as i do, i'll let you (and anyone else) know if i arrived at the correct answer.


thanks,
Eric

 

[CompuChip]

Good luck with that, I hope you get it right then (mostly because I don't look forward to going through all that to find another error on the last line :) )

Cheers

 

[94JZA80]

good news...the simple mistake you caught was the one and only error i overlooked. sure enough, taking into account that the derivative of 8 is 0, all the algebra works out accordingly to give the correct answer of y'' = 64/(3x + y)³ :

[PLAIN]http://img696.imageshack.us/img696/4379/scan0001med.jpg


thanks for the help CompuChip. sometimes you just have to walk away from something in order to clear your mind and look at it again with a fresh set of eyes...either that, or have someone else's fresh set of eyes to look at it for you if you don't have the time/patience .