3 Attachment(s)

Implicit Differentiation issue

I'm not sure if I just hit my limit for the day regarding Calc, but I may have. I was wondering if someone could take a look at this problem for me. I have the solution in front of me, with most of the steps, but I don't see how to go from the last step to the conclusion.

The problem is stated:

If x^2-xy+y^2=3, find y' and y".

2x-xy'-y+2yy'=0

Attachment 28826

I just don't see how to go from the

Attachment 28827

to 18/(x-2y)^3

Is there something that is incredibly obvious that I am missing, or is it just another problem with this book? (I have found a few errors already)

Thank you! Any input would be appreciated.

Re: Implicit Differentiation issue

Hello, jman242!

Hope you have a sense of humor.

Quote:

$\displaystyle \text{Given: }\:x^2-xy+y^2\:=\:3.\quad\text{Find }y'\text{ and }y".$

$\displaystyle \text{I just don't see how to go from }\:\frac{6(x^2-xy+y^2)}{(x-2y)^3}\:\text{ to }\:\frac{18}{(x-2y)^3}$

Look at the "Given" . . .

We were *told* that:-$\displaystyle x^2-xy+y^2$ is equal to $\displaystyle 3.$ . . *facepalm*

Get it?

Watch for this . . .

It turns up in many Implicit Differentiaton problems.

Re: Implicit Differentiation issue

I will admit I chuckled over what was my confusion. I always love tutoring someone and making them see their own error and then point out I do the same exact mistakes. Thanks Soroban. I wish you could have seen my face when I understood, I know you would have laughed. Cheers, and to more mathemagical humor in the future...