$\"\"$

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The volume $\"\"$ of the water remaining in the tank after $\"\"$ minutes is $\"\"$ , $\"\"$ .

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The rate at which water is draining from the tank $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$ .

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Chain rule of derivatives: $\"\"$ .

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$\"\"$

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(a)

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Rate at which water is draining from the tank after $\"\"$ min :

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$\"\"$

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Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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$\"\"$

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(b)

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Rate at which water is draining from the tank after $\"\"$ min :

\

$\"\"$

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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$\"\"$

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(c)

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Rate at which water is draining from the tank after $\"\"$ min :

\

$\"\"$

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Her negative sign indicates that the level of the water in the tank was decreases.

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Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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$\"\"$

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(d)

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Rate at which water is draining from the tank after $\"\"$ min is

\

$\"\"$

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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$\"\"$

\

(a) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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(b) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

(c) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

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(d) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.