Find a potential for the given vector field: $$\vec { F } ( x , y ) = \left\langle 3 x ^ { 2 } \cos ( x y ) - x ^ { 3 } y \sin ( x y ) , - x ^ { 4 } \sin ( x y ) \right\rangle$$
A) $f ( x , y ) = x ^ { 4 } \cos ( x y )$
B) $f ( x , y ) = x ^ { 3 } \sin ( x y )$
C) $f ( x , y ) = x ^ { 3 } \cos ( x y )$
D) $f ( x , y ) = x ^ { 4 } \sin ( x y )$

Question

Quizplus · Accepted Answer

The Answer is C

Find a Potential for the Given Vector Field F⃗(x,y)=⟨3x2cos⁡(xy)−x3ysin⁡(xy),−x4sin⁡(xy)⟩\vec { F } ( x , y ) = \left\langle 3 x ^ { 2 } \cos ( x y ) - x ^ { 3 } y \sin ( x y ) , - x ^ { 4 } \sin ( x y ) \right\rangleF(x,y)=⟨3x2cos(xy)−x3ysin(xy),−x4sin(xy)⟩

Find a Potential for the Given Vector Field $\vec { F } ( x , y ) = \left\langle 3 x ^ { 2 } \cos ( x y ) - x ^ { 3 } y \sin ( x y ) , - x ^ { 4 } \sin ( x y ) \right\rangle$