# Thread: Is this wrong? (differential operator)

1. ## Is this wrong? (differential operator)

I believe this soln has an error.

Am I right?

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

Am I right?
What is $\displaystyle F$? What are $\displaystyle x$ and $\displaystyle y$?

3. Sorry, I didn't think it mattered, given the context. But here they are:

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

(Also, we assume the mixed derivatives are equal)

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

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

(Also, we assume the mixed derivatives are equal)
We needed to know that $\displaystyle x=x(s),y=y(s)$

And so you're just applying the chain rule? That is what that jpeg is of, right? Double application of the chain rule?

5. Isn't x = x(s, t) and y = y(s, t)?

Yes, this is the chain rule for partial derivs.