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

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)