💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 1 Easy Difficulty

Find the derivative of $ f(x) = (1 + 2x^2)(x - x^2) $ in two ways: by using the Product Rule and by performing the multiplication first. Do your answer agree?


$f^{\prime}(x)=1-2 x+6 x^{2}-8 x^{3}$

More Answers


You must be signed in to discuss.

Video Transcript

it's clear. So when you right here, So we're first going to use the product roll we get one plus two x square derivative X minus X square, plus one plus two X square times the derivative of X minus X square. Then we get zero plus four x times X minus X square plus one plus two X square times one minus two x We simplify. Let me go! Negative B X cube plus six X square minus two X plus one. Now we're gonna differentiate by multiplying everything out and then differentiating them separately. So we get X minus X square plus two x cubed minus two X plus two X cubed minus two x to the fourth. We do d y over DX, then we get negative eight x cubed Last six X square minus two x plus one