Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$ Find a function $F_{2}(x, y)$ , such that $\vec{F}=F_{1} \vec{i}+F_{2} \vec{j}$ is a gradient field.

Name: Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$ Find a function $F_{2}(x, y)$ , such that $\vec{F}=F_{1} \vec{i}+F_{2} \vec{j}$ is a gradient field.
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The Answer of Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$ Find a function $F_{2}(x, y)$ , such that $\vec{F}=F_{1} \vec{i}+F_{2} \vec{j}$ is a gradient field.

Let F1(x,y)=y5−10xy+cos⁡yF _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos yF1​(x,y)=y5−10xy+cosy

Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$