Final answer:
To calculate the derivative of s(x) = (3x - 9)(2x + 8), we use the product rule. The derivative, s'(x), is found to be 12x + 6.
Step-by-step explanation:
To find the derivative of the function s(x) = (3x - 9)(2x + 8), we need to apply the product rule which states that the derivative of two functions multiplied together is the first function times the derivative of the second plus the second function times the derivative of the first. So, let's label the two parts of our function: f(x) = 3x - 9 and g(x) = 2x + 8. Now, we find the derivatives f'(x) = 3 and g'(x) = 2.
Applying the product rule, we get:
s'(x) = f'(x)g(x) + f(x)g'(x) = (3)(2x + 8) + (3x - 9)(2) = 6x + 24 + 6x - 18.
Simplify to combine like terms:
s'(x) = 12x + 6.The derivative of the function s(x) is 12x + 6.