Find the four second partial derivatives.Observe that the second mixed partials are equal.

Question

Find the four second partial derivatives.Observe that the second mixed partials are equal. ​  ​

Quizplus · Accepted Answer

The four second partial derivatives are:

fxx = 11ea8970_6a8c_400d_861b_cf5c1c066ba5_TB1301_11
fxy = fyx = 11ea8970_6a8c_400e_861b_95b07c7f4c77_TB1301_11
fyy = 11ea8970_6a8c_400f_861b_e173d559a464_TB1301_11
fxz = fzx = fyz = fzy = 11ea8970_6a8c_4010_861b_bfdb0ca41972_TB1301_11

From the given observation that the second mixed partials are equal, we can see that fxy = fyx, fxz = fzx, and fyz = fzy. The only answer choice that has this pattern is C.

Find the Four Second Partial Derivatives