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Easy: Squares
Write the formula that links the quantities, then differentiate both sides with respect to time t, using the chain rule on every variable that changes. Substitute the values at the moment asked about only after differentiating, then solve for the unknown rate.
Find the rate. Give answers with π in terms of π.
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After differentiating. If you plug in the radius before differentiating, it becomes a constant and its rate of change is lost.
Both A and r depend on time, so differentiating A = πr² with respect to t uses the chain rule: dA/dt = 2πr · dr/dt.
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