Is this wrong? (differential operator)

• Jun 4th 2010, 07:38 PM
scorpion007
Is this wrong? (differential operator)
I believe this soln has an error.

http://img44.imageshack.us/img44/448/math28.png

Am I right?
• Jun 4th 2010, 08:47 PM
Drexel28
Quote:

Originally Posted by scorpion007
I believe this soln has an error.

http://img44.imageshack.us/img44/448/math28.png

Am I right?

What is $F$? What are $x$ and $y$?
• Jun 4th 2010, 08:54 PM
scorpion007
Sorry, I didn't think it mattered, given the context. But here they are:

http://img192.imageshack.us/img192/4918/math29.png

The reason I say it's wrong is because when you distribute the x through the first term, you end up with $x^2$ and similarly for the second term with y.

(Also, we assume the mixed derivatives are equal)
• Jun 4th 2010, 09:04 PM
Drexel28
Quote:

Originally Posted by scorpion007
Sorry, I didn't think it mattered, given the context. But here they are:

http://img192.imageshack.us/img192/4918/math29.png

The reason I say it's wrong is because when you distribute the x through the first term, you end up with $x^2$ and similarly for the second term with y.

(Also, we assume the mixed derivatives are equal)

We needed to know that $x=x(s),y=y(s)$

And so you're just applying the chain rule? That is what that jpeg is of, right? Double application of the chain rule?
• Jun 4th 2010, 09:11 PM
scorpion007
Isn't x = x(s, t) and y = y(s, t)?

Yes, this is the chain rule for partial derivs.