Qual é a derivada de (x-1) (x ^ 2 + 2) ^ 3 (x−1)(x2+2)3?
Responda:
(x^2+2)^2(7x^2-6x+2)(x2+2)2(7x2−6x+2)
Explicação:
"differentiate using the "color(blue)"product rule"differentiate using the product rule
"given "y=g(x).h(x)" then"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)