найдите производную[tex]y = \frac{1}{x \sqrt{2x} } [/tex][tex]y = \frac{ \sqrt{x} }{x \sqrt[3]{x} } [/tex]. Created by Tatiana118190. algebra-ru

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Tatiana118190 @Tatiana118190

June 2022 1 4 Report

найдите производную
[tex]y = \frac{1}{x \sqrt{2x} } [/tex]
[tex]y = \frac{ \sqrt{x} }{x \sqrt[3]{x} } [/tex]

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$1)\; \; y= \frac{1}{x \sqrt{2x} }= \frac{1}{\sqrt2\cdot \sqrt{x^3}}= \frac{1}{\sqrt2} x^{-\frac{3}{2}}\\\\y'=\frac{1}{\sqrt2}\cdot (- \frac{3}{2})\cdot x^{-\frac{5}{2} }=-\frac{3}{2\sqrt2 \cdot \sqrt{x^5} } \\\\2)\; \; y= \frac{ \sqrt{x} }{x \sqrt[3]{x} } =\frac{x^{1/2}}{x\cdot x^{1/3}}= \frac{x^{1/2}}{x^{4/3}}=x^{ \frac{1}{2}-\frac{4}{3} }=x^{-\frac{5}{6}}\\\\y'=- \frac{5}{6}\cdot x^{-\frac{11}{6}}=-\frac{5}{6\cdot \sqrt[6]{x^{11}}}$

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