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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?

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

01:47

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Nottingham

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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

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