$\"\"$

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Differentiation rule :

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Suppose $\"\"$ and $\"\"$ are differentiable vector functions, $\"\"$ is a scalar and $\"\"$ is a real valued function.

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Then $\"\"$ . $\"\"$

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The vectors are $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$ .

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$\"\"$

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Substitute coresponding values in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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$\"\"$ .