Question

Find the derivative of f(x)=(1+7x^2)(x-x^2) by using the product rule and by multiplying first.

Answer 1

multiplying first:
y = x + 7 x^3 - x^2 -7 x^4
so
dy/dx = 1 + 21 x^2 - 2 x - 28 x^3

Product rule
(1+7x^2)(1-2x) + (x-x^2)(14x)

=1 +7 x^2 -2 x -14 x^3 +14 x^2 - 14 x^3

= 1 + 21 x^2 - 2 x -28 x^3 luckily the same

Answer 2

or, just to make things complete, factor and then use the product rule:

f(x) = x(1-x)(1+7x^2)
f'(x) = (1-x)(1+7x^2) + x(-1)(1+7x^2) + x(1-x)(14x)
= 1 - 2x + 21x^2 - 28x^3