Question

deriva la función: $y=\sqrt[3]{x^{3}+2 }$

Answer 1

$y \: = \: \sqrt[3]{x^{3} \: + \: 2 }$

$y' \: = \: \frac{d}{dx} ( \sqrt[3]{ {x}^{3} \: + \: 2}$

$y' \: = \: \frac{d}{dx} (( {x}^{3} \: + \: 2) ^{ \frac{1}{3} } )$

$y' \: = \: \frac{d}{dg} ( {g}^{ \frac{1}{3} } ) \: \times \: \frac{d}{dx} ( {x}^{3} \: + \: 2)$

$y' \: = \: \frac{1}{3} g ^{ - \frac{2}{3} } \: \times \: {3x}^{2}$

$y' \: = \: \frac{1}{3} \: \times \: ( {x}^{3} \: + \: 2) ^{ - \frac{2}{3} } \: \times \: {3x}^{2}$

$\boxed{ \bold{y' \: = \: \frac{ {x}^{2} }{ \sqrt[3]{( {x}^{3} \: + \: 2) ^{2} } } }}$

Besitos OvO