Which of the Following Could Represent a Function, F(x, Y) $\frac { \partial f } { \partial x } = 3 x y ( x y + 2 ) \quad \frac { \partial f } { \partial y } = x ^ { 2 } ( 2 x y + 3 )$

Multiple Choice

Which of the following could represent a function, f(x, y) , with first- order partial derivatives?
$\frac { \partial f } { \partial x } = 3 x y ( x y + 2 ) \quad \frac { \partial f } { \partial y } = x ^ { 2 } ( 2 x y + 3 )$

A) $x ^ { 3 } y ^ { 2 } + 3 x ^ { 2 } y - 6$

B) $x y \left( x ^ { 2 } y + 3 \right)$

C) $x ^ { 3 } y ^ { 2 } + 2 x ^ { 2 } y ^ { 3 } + 1$

D) $x ^ { 2 } \left( x y ^ { 2 } + 3 \right)$

E) none of these