Final answer:
To find the derivative of the function y=(x+8)(x-1)(x²+3), we apply the product rule and the power rule of differentiation, and sum up the derivatives of each pair of functions.
Step-by-step explanation:
The derivative of a given function y=(x+8)(x-1)(x²+3). To find the derivative of this function, we must use the product rule and the power rule of differentiation. The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. For products of more than two functions, this rule gets applied multiple times. Additionally, the power rule states that the derivative of x raised to the power of n is n times x raised to the power of n-1.
Applying these rules iteratively, the derivative of the given function is a combination of derivatives of each pair of functions, while treating the third as a constant during each differentiation step. Ultimately, we will sum up all these individual products ensuring we have taken into account each function's change in respect to x.