What is the derivative of $f (x) = (x - 1) (x - 2) (x - 3)$ $f(x)=(x-1)(x-2)(x-3)$ ?

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Answer 1 · 2016-08-11T18:13:52

$f'(x)=3x^2-12x+11$ .

I will describe 2 Methods to solve the problem.

Method I :-

We use the Multiplication Rule for Differentiation # :

$(uvw)'=u'vw+v'uw+uvw'$

Hence, $f'(x)=(x-1)'(x-2)(x-3)+(x-1)(x-2)'(x-3)+(x-1)(x-2)(x-3)'$

$=(x-2)(x-3)+(x-1)(x-3)+(x-1)(x-2)$

$f'(x)=3x^2-12x+11$ .

Method II :-

Given, $f(x)=(x-1)(x-2)(x-3)=x^3-6x^2+11x-6$ .

Hence, $f"(x)=3x^2-12x+11$ , as Before!

Enjoy Maths.!

What is the derivative of f(x)=(x-1)(x-2)(x-3)f(x)=(x−1)(x−2)(x−3)f(x)=(x-1)(x-2)(x-3)?