Find the Divergence of the Vector Field F Given By \mathbf

Multiple Choice

Find the divergence of the vector field F given by $$\mathbf { F } ( x , y , z ) = \sin ( 7 x ) \mathbf { i } + \cos ( 6 y ) \mathbf { j } + z ^ { 3 } \hat { \mathbf { k } }$$

A) $7 \cos ( x ) - 6 \sin ( y ) + 3 z ^ { 2 }$
B) $\cos ( x ) + \sin ( y ) + z ^ { 4 }$
C) $7 \cos ( 7 x ) + 6 \sin ( 6 y ) + 3 z ^ { 4 }$
D) $7 \cos ( 7 x ) - 6 \sin ( 6 y ) + 3 z ^ { 2 }$
E) $\cos ( 7 x ) - \sin ( 6 y ) + z ^ { 2 }$