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