Question

Rezolvati cu regula produceri!

Answer 1

Răspuns:

Explicație pas cu pas:

$\dfrac{d}{dx}\Big[x(x\ -\ 2)^2\Big] =\\\\=x*\dfrac{d}{dx}\Big(x\ -\ 2\Big)^2 + \Big(x\ -\ 2\Big)^2*\dfrac{d}{dx}\Big(x\Big) =\\\\= x*\Big[2*\Big(x\ -\ 2\Big)\Big] + \Big(x\ -\ 2\Big)^2*1 = \\\\= 2x*\Big(x\ -\ 2\Big) + \Big(x\ -\ 2\Big)^2 = \\\\=\Big(x\ -\ 2\Big)*\Big[2x + \Big(x\ -\ 2\Big)\Big] = \\\\=\Big(x\ -\ 2\Big)*\Big(3x\ -\ 2\Big) =\\\\= 3x^2 - 2x - 6x + 4 =\\\\= 3x^2 - 8x + 4$

Answer 2

$\it [x(x-2)^5]'=x'(x-2)^5+x[(x-2)^5]'=1(x-2)^5+x\cdot 5(x-2)^4=\\ \\ =(x-2)^5+5x(x-2)^4=(x-2)^4(x-2+5x)=(x-2)^4(6x-2)$