Question

CPOЧНО!!!
Найдите производную функции:
У=х^2(х-2)^2

Answer 1

y = x^2 *(x - 2)^2 

y ' = (x^2)' (x - 2)^2 + ((x -  2)^2)' x^2 = 
= 2x(x - 2)^2 + 2x^2*(x - 2) = 
 = 2x (x^2  - 4x + 4) + 2x^3 - 4x^2 = 
= 2x^3 - 8x^2 + 8x + 2x^3 - 4x^2 = 
= 4x^3 - 12x^2 + 8x = 
= 4x (x^2 - 3x + 2)