7.
|
A. –xy2cos(xy)-2y sin(xy) |
B. –x2ysin(xy)-2y sin(xy) |
C. –x2y sin(xy)-2xcos(xy) |
|
D. –x2y sin(xy) |
E. –xy2cos(xy) |
Solution: The answer is A
Since,
Which says, take the partial derivative with respect to x of the partial derivative with respect to x of the partial derivative with respect to y of sin(xy). Thus, taking the partial derivatives in the reverse order will generate the solution.
The partial derivative with respect to y of sin(xy) is,
The partial derivative with respect to x of the above result is,
The partial derivative with respect to x of the above result is,
