A lot, of course, depends on the function f(x,y).
Define .
Then .
Now, so that .
.
I found this question on Yahoo! Answers, and I am stumped (however, I would like to know the answer):
Let f(x,y) be a continuous function in R2. For t>0 let R_t = [0,t] x [0,2t] = { (x,y) | 0<=x<=t, 0<=y<=2t }
and define F(t) integral integral R_t of f(x,y)dA
Use Leibniz Rule to compute the derivative dF/dt.
Here's the link:
How do I use Leibniz Rule? - Yahoo! Answers
Thanks, Charles
Are you sure you didn't intend to write:
Anyway, your formula didn't work when I set f(x,y) = x sin y, although perhaps I made a mistake in my calculation. Are you sure your formula is correct?
Also, I don't understand why you have two terms in your result: G(t,t) and