What is the derivative of #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.!