Derivative problem

[AGlas9837]

I have a given (first) derivative of (x-2)^3 (x-1) which is (4x-5) (x-2)^2. I tried using the product rule to arrive at this answer but didn't get:

(x-2)^3 (1) + (x-1) 3(x-2)^2

(x-2)^3 + (x-1) (3) (x^2-4x+4)

(x-2) (x^2-4x+4) + (x-1) (3) (x^2-4x+4)

Is any of this correct so far?!

 

[royhaas]

It's correct but you should factor (x-2)^2 as the second step, then simplify to get the final result. In other words, there's no reason to expand (x-2)^2.