Find the derivative of f (x) = (1 + 6x2) (x - x2) in two ways.

Using product rule;

f (x) = (1+6x²) (x-x²)

f' (x) = (12x) (x-x²) + (1-2x) (1+6x²) = 12x² - 12x³ + 1 + 6x² - 2x - 12x³ = - 24x³ + 18x² - 2x + 1

Solving the bracket first;

f (x) = (1+6x²) (x-x²) = x - x² + 6x³ - 6x^4

f' (x) = 1 - 2x + 18x² - 24x³ = - 24x³ + 18x² - 2x + 1