Нужно найти производную[tex]y = \sqrt[4]{3 x^{3} } - \sqrt[3]{2x} + \sqrt[]{2 x^{3} } [/tex]. Created by tirelessly. algebra-ru

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August 2022 1 17 Report

Нужно найти производную
[tex]y = \sqrt[4]{3 x^{3} } - \sqrt[3]{2x} + \sqrt[]{2 x^{3} } [/tex]

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Anastsiia $y'=( \sqrt[4]{3x^3}-\sqrt[3]{2x}+\sqrt{2x^3})'=\sqrt[4]{3}(x^{\frac{3}{4}})'-\sqrt[3]{2}(x^{\frac{1}{3} })'+\sqrt{2}(x^{\frac{3}{2}})'=\\=\sqrt[4]{3}*\frac{3}{4}*x^{\frac{3}{4}-1}-\sqrt[3]{2}*\frac{1}{3}x^{ \frac{1}{3}-1 }+ \sqrt{2}* \frac{3}{2}* x^{\frac{3}{2}-1}=\\=\frac{3\sqrt[4]{3}}{4}*x^{-\frac{1}{4}}- \frac{\sqrt[3]{2}}{3}x^{ -\frac{2}{3}}+ \frac{3\sqrt{2}}{2}*x^{\frac{1}{2}}=


$
$=\frac{3\sqrt[4]{3}}{4x^{\frac{1}{4}}}- \frac{\sqrt[3]{2}}{3x^{\frac{2}{3}}}+ \frac{3\sqrt{2}}{2} \sqrt{x}=\frac{3\sqrt[4]{3}}{4 \sqrt[4]{x} }- \frac{\sqrt[3]{2}}{3 \sqrt[3]{ x^{2} } }+ \frac{3\sqrt{2}}{2} \sqrt{x}$

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