Dezembro 25, 2019

por Dona

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

Responda:

${(x^{2} + 2)}^{2} (7 x^{2} - 6 x + 2)$ $(x^2+2)^2(7x^2-6x+2)$

Explicação:

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

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

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

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

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

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

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

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

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