Final answer:
The double derivative of -8(x^2 + 3)^3 requires first finding the first derivative with the chain rule and then differentiating again, using the product rule for the second step.
Step-by-step explanation:
The question asks for the double derivative of the function -8(x2 + 3)3. To find the double derivative, we must find the first derivative and then differentiate it again. Using the chain rule, the first derivative of the function is -48(x2 + 3)2 × 2x. We then take the derivative of this result to find the second derivative.
The second derivative, also known as the double derivative, would involve applying the product rule to the first derivative's result, resulting in a more complex expression containing powers of x and constants. The process highlights the significance of understanding derivatives and their role in understanding the behavior of functions in mathematics, particularly in calculus.