Question

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

Answer 1

A' = 6(3t +1)

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)