3. Let u(x,y,z) = 1/(x2 + y2 + z2)1/2 for x, y, z not all zero. Then
|
A. 0 |
B. 1 |
C. –(x+y+z)/(x2+y2+z2)1/2 |
|
D. (9/2)(x2 + y2 + z2)-5/2 |
E. (x2 + y2 + z2)-2 |
Solution: The answer is A
Find the partial derivative of u with respect to x, by rewriting u and using the Chain Rule, as follows:
Use the Product Rule and the Chain Rule to take the partial derivative with respect to x of both sides of the above equation.
Similarly,
Thus,
