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7 September, 00:59

A square with side x, is changing with time where x (t) = 3t+1. What is the formula for the rate of change of the area of the square

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  1. 7 September, 01:14
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    A' = 6 (3t + 1)

    Step-by-step explanation:

    The area is the square of the side length, so ...

    A = (3t + 1) ²

    The derivative with respect to t is then

    A' = 2 (3t + 1) · (3) = 6 (3t + 1)

    If you like, you can multiply out the area expression first, then differentiate.

    A = 9t² + 6t + 1

    A' = 18t + 6

    This can be factored, if you like, to ...

    A' = 6 (3t + 1)
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