Question

Помогите найти производную функцию.

Answer 1

Ответ:

y' = ((6x^2 + 5x)^(1/3))' =  1/3 * (6x^2 + 5x)^(-2/3) * (6x^2 + 5x)' =

1/3 * (6x^2 + 5x)^(-2/3) * (12x + 5) = (6x^2 + 5x)^(-2/3) * (4x + 5/3) =

(4x + 5/3) / $\sqrt[3]{(6x^2 + 5x)^{2} }$ =

Answer 2

$y=\sqrt[3]{6x^{2}+5x } =(6x^{2}+5x)^{\frac{1}{3} } \\\\y'=\Big[(6x^{2}+5x)^{\frac{1}{3} }\Big]'=\dfrac{1}{3} (6x^{2}+5x)^{-\frac{2}{3} }\cdot(6x^{2}+5x)'= \\\\=\dfrac{1}{3} (6x^{2}+5x)^{-\frac{2}{3} }\cdot(12x+5)=\dfrac{1}{3}\cdot\dfrac{1}{\sqrt[3]{(6x^{2} +5x)^{2} } }\cdot(12x+5)=\\\\=\boxed{\dfrac{12x+5}{3\sqrt[3]{(6x^{2}+5x)^{2}} }}$