производная2........................ Created by AnyGool. algebra-ru

производная2...

Chemist0 $y=\sqrt[3]{x^5} =x^{\frac{5}{3}}\; ,\; \; \; \; \; (x^{n})'=n\cdot x^{n-1}\\\\n=\frac{5}{3}\; ,\; \; \; y'=\frac{5}{3}\cdot x^{\frac{5}{3}-1}=\frac{5}{3}\cdot x^{\frac{2}{3}}=\frac{5}{3}\cdot \sqrt[3]{x^2}$

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NNNLLL54 А дальше надо преобразовать степени.

NNNLLL54

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$y = \sqrt[3]{x^5} 

y` = (\sqrt[3]{x^5} )` = \frac{(x^5)`}{3(x^5)^ \frac{2}{3} }$
$y` = \frac{5x^4}{3(x^5)^ \frac{2}{3} }$

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