Question

como calcular a derivada de y=(x3 – 1).(6x2 +1)

Answer 1

$y=(x^3-1)\cdot (6x^2+1)$

Derivando usando a Regra do Produto:

$\dfrac{dy}{dx}=\dfrac{d}{dx}(x^3-1)\cdot (6x^2+1)+(x^3-1)\cdot \dfrac{d}{dx}(6x^2+1)\\\\\\ \dfrac{dy}{dx}=(3x^{3-1}-0)\cdot (6x^2+1)+(x^3-1)\cdot (6\cdot 2x+0)\\\\\\ \boxed{\begin{array}{c}\dfrac{dy}{dx}=3x^2\cdot (6x^2+1)+(x^3-1)\cdot 12x \end{array}}$