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.

Look at the "Given" . . .

We were *told* that:- is equal to . . *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...