Question

Найти производную функций

Answer 1

Ответ:

$1) \ y=x^3(4+2x-x^2)\ \ ,\ \ \ y'=3x^2(4+2x-x^2)+x^3(2-2x)\\\\2)\ \ y=x^2(3x+x^3)=3x^3+x^5\ \ ,\ \ \ y'=9x^2+5x^4\\\\3)\ \ y=(2x-3)(1-x^3)\ \ ,\ \ \ y'=2(1-x^3)-3x^2(2x-3)\\\\4)\ \ y=6x^3(4+2x-3x^2)\ \ ,\ \ y'=18x^2(4+2x-3x^2)+6x^3(2-6x)\\\\5)\ \ y=(4x-3)(6+x^3)\ \ ,\ \ \ y'=4(6+x^3)+3x^2(4x-3)\\\\6)\ \ y=(x-3)(-5x^3)=-5x^3-15x^2(x-3)=-20x^3+45x^2\\\\7)\ \ y=x(x+1)=x^2+x\ \ ,\ \ \ y'=2x+1\\\\8)\ \ y=(2x-3)(6x-x^3)\ \ ,\ \ y'=2(6x-x^4)+(2x-3)(6-3x^2)$