To find the derivative of the function y = 8x^3 - x^2, we should apply the power rule, which states that the derivative of x^n, regarding x, is n*x^(n-1).
The power rule can be applied to each term of the function separately.
First, let's take the term 8x^3.
According to the power rule, the derivative of x^3 is 3*x^2. Multiply this by 8, as the original term was 8x^3, the derivative would be 24x^2.
Now, let's look at the term -x^2.
Apply the power rule again, the derivative of x^2 is 2*x^1 (or just 2x). Since the original term was -x^2, the derivative of this term is -2x.
Add these two terms together, the derivative of 8x^3 - x^2 will be 24x^2 - 2x. This function, y' = 24x^2 - 2x, represents the rate of change at any point along the curve of the original function.