Question

Derivada composta de y = raiz cubica de 6x² + 7x + 2

Answer 1

Olá

$y= \sqrt[3]{6x^2+7x+2} \\ \\ Reescrevendo~em~forma~de~potencia \\ \\ y=(6x^2+7x+2)^ \frac{1}{3} \\ \\ Derivando \\ \\ y'= \frac{1}{3}(6x^2+7x+2)^ \frac{1}{3}^-^1~\cdot (6\cdot2x^2^-^1+7x^1^-^1+0) \\ \\ y'= \frac{1}{3}(6x^2+7x+2)^-^ \frac{2}{3}~\cdot(12x+7) \\ \\ y'= \frac{1}{3(6x^2+7x+2)^ \frac{2}{3} } \cdot (12x+7) \\ \\ \\ Voltando~ pra ~forma ~de~ raiz$

$y'= \frac{1}{3 \sqrt[3]{6x^2+7x+2)^2} } \cdot (12x+7) \\ \\ \\ \boxed{\boxed{y'= \frac{12x+7}{3 \sqrt[3]{(6x^2+7x+2)^2} } }}$