Qual é a derivada de (x-1) (x ^ 2 + 2) ^ 3 ?

Responda:

(x^2+2)^2(7x^2-6x+2)

Explicação:

"differentiate using the "color(blue)"product rule"

"given "y=g(x).h(x)" then"

dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"

g(x)=x-1rArrg'(x)=1

h(x)=(x^2+2)^3rArrh'(x)=3(x^2+2)^2.d/dx(x^2+2)

color(white)(xxxxxxxxxxxxxxxxxx)=6x(x^2+2)^2

rArrdy/dx=6x(x-1)(x^2+2)^2+(x^2+2)^3

color(white)(rArrdy/dx)=(x^2+2)^2(6x^2-6x+x^2+2)

color(white)(rArrdy/dx)=(x^2+2)^2(7x^2-6x+2)