Final answer:
The rate of change of the expression y=(3x+1)−²-1 is found by differentiating it with respect to x. The derivative is -6(3x+1)−³, which tells us how the value of y changes as x changes.
Step-by-step explanation:
The given expression is y=(3x+1)−²-1. To determine how fast this percent change is, or in mathematical terms, the rate of change, you'll need to differentiate the expression with respect to x. The rate of change tells us how the value of y changes concerning a change in x. A differentiation will give us dy/dx, which represents this rate of change.
If the expression is meant to be (3x+1)^(-2) - 1, and we need to find its derivative, we use the power rule for differentiation combined with the chain rule. The derivative of (3x+1)^(-2) with respect to x is -2(3x+1)^(-3) × 3, and the derivative of a constant like -1 is 0. Therefore, the derivative or rate of change of the expression with respect to x is -6(3x+1)^(-3).
This tells us how the value of y changes for a small change in x, and thus how 'fast' the percent change is happening, if by percent change we refer to the relative change with respect to x.