Final answer:
The rate of change of volume with respect to the surface of the square is -8wx.
Step-by-step explanation:
The question is asking for the rate of change of volume with respect to the surface of a square. We are given the equation v=w(-2x)². To find the rate of change of volume, we need to find dv/dx, which represents the derivative of volume with respect to the side length of the square.
Using the power rule of differentiation, we can find the derivative of v with respect to x. The derivative of (-2x)² is 4(-2x). Multiplying this by w, we get the derivative of v as -8wx.
Therefore, the rate of change of volume with respect to the surface of the square is -8wx.