Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 + y2)2 , on the region where (x, y) ≠ (0, 0) verify the following theorem in this case. if f(x, y) is of class c2 (is twice continuously differentiable), then the mixed partial derivatives are equal; that is, ∂2f ∂x ∂y = ∂2f ∂y ∂x .

[15 points, algebra 2]simplify the complex fraction and find the restrictions.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Askyscraper is 396 meters tall. at a certain time of day, it casts a shadow that is 332 meters long. at what angle is the sun above the horizon at that time?