Find the derivative of f (x) = (1 + 5x2) (x - x2) in two ways. use the product rule. f ' (x) = perform the multiplication first. f ' (x) = do your answers agree? yes no

The product rule states that given a function:

f (x) = g (x) h (x)

f' (x) = g' (x) h (x) + h' (x) g (x)

thus the derivative of the expression will be given by:

f (x) = (1 + 5x2) (x - x2)

g (x) = (1+5x^2)

g' (x) = 10x

h (x) = (x-x^2)

h' (x) = 1-2x

thus:

f' (x) = 10x (x-x^2) + (1-2x) (1+5x^2)

simplifying this we get:

f' (x) = - 20x^3+15x^2-12x+1