$\"\"$

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The function is $\"\"$ , point is $\"\"$ and vector is $\"\"$ .

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(a)

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Find gradient of $\"\"$ .

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The gradient of the function $\"\"$ is the vector function of $\"\"$ , then $\"\"$ .

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Consider $\"\"$ .

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Apply partial derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply partial derivative on each side with respect to $\"\"$ .

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$\"\"$

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Then the gradient vector of $\"\"$ is $\"\"$ .

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$\"\"$

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(b)

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Find the gradient vector at a point $\"\"$ .

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Substitute $\"\"$ in the gradient vector.

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$\"\"$

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The gradient vector at a point $\"\"$ is $\"\"$ .

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$\"\"$

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(c)

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The rate of change of the function $\"\"$ in the direction of a vector u is $\"\"$ .

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The vector $\"\"$ and a point is $\"\"$ .

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The rate of change of the function $\"\"$ at a point $\"\"$ in the direction of a vector u is

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$\"\"$

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .