$\"\"$

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The function is $\"\"$ .

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Definition of conservative :

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In a vector field $\"\"$ , if $\"\"$ then F is conservative.

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The function is $\"\"$ .

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$\"\"$

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$\"\"$

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Here $\"\"$ .

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So F is conservative.

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$\"\"$

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If F is conservative, then find the potential function for $\"\"$ .

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To find the potential function, follow the condition $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ equation (1)

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$\"\"$

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$\"\"$

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$\"\"$ equation (2)

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From equation (1) and equation (2), $\"\"$ .

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$\"\"$

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F is conservative.

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The potential function is $\"\"$ .