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).(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Given the equation x^{2}+6xy + y^{2}= 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(x^{2}+6xy + y^{2}), 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.

2. Relevant equations

see section 3 below...

3. The attempt at a solution

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

...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

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# Homework Help: Basic calc I problem: calculate y''

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