$\"\"$

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The function is $\"\"$ , point at $\"\"$ and angle is $\"\"$ .

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Consider $\"\"$ .

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Apply partial derivative on each side with respect to x.

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$\"\"$

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Substitute $\"\"$ in the $\"\"$ .

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$\"\"$

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Apply partial derivative on each side with respect to y.

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$\"\"$

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Substitute $\"\"$ in the $\"\"$ .

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$\"\"$

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$\"\"$

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The directional derivative in the direction of a unit vector $\"\"$ then

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$\"\"$ .

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The directional derivative of the function at a point $\"\"$ in the direction $\"\"$ is

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$\"\"$

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$\"\"$ .

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$\"\"$

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The directional derivative of the function is $\"\"$ .