Calculus of a Single Variable, Chapter 2, Review, Section Review, Problem 29

You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that:
f'(x) = (5x^2 + 8)'(x^2 - 4x - 6) + (5x^2 + 8)(x^2 - 4x - 6)'
f'(x) = (10x + 0)(x^2 - 4x - 6) + (5x^2 + 8)(2x - 4 - 0)
f'(x) = 10x(x^2 - 4x - 6) + (2x - 4)(5x^2 + 8)
f'(x) = 10x^3 - 40x^2 - 60x + 10x^3 + 16x - 20x^2 - 32
Combining like terms yields:
f'(x) = 20x^3 - 60x^2 - 44x - 32
Hence, evaluating the derivative of the function, using the product rule, yields f'(x) = 20x^3 - 60x^2 - 44x - 32.