Let $\vec { F } = \frac { y } { 4 x ^ { 2 } + 4 x y + y ^ { 2 } } \vec { i } - \frac { x } { 4 x ^ { 2 } + 4 x y + y ^ { 2 } } \vec { j }$

question 53

Essay

Let $\vec { F } = \frac { y } { 4 x ^ { 2 } + 4 x y + y ^ { 2 } } \vec { i } - \frac { x } { 4 x ^ { 2 } + 4 x y + y ^ { 2 } } \vec { j }$ Check that $\frac { \partial F _ { 1 } } { \partial y } = \frac { \partial F _ { 2 } } { \partial x }$ .Is $\vec{F}$ is path-independent?

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