The required expression gives the rate of change will be d'(3) at which the depth is changing at 3 minutes.
Let d(t) represent the depth of the rain puddle at any time t,
⇒ d(t) ....(i)
The depth is changing with respect to time, which is given in the question
Differentiate equation (i) with respect to t and we get
⇒ δd(t)/δt = d'(t) ....(ii)
This is the rate of change in depth unit time
As per the question, the depth is changing at 3 minutes
Substitute the value of t = 3 in equation (ii), and we get
⇒ d'(3)
Therefore, the required expression gives the rate of change will be d'(3).
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