Question

найдите производную
$y = frac{1}{x sqrt{2x} }$
$y = frac{ sqrt{x} }{x sqrt[3]{x} }$

Answer 1

$1); ; y= frac{1}{x sqrt{2x} }= frac{1}{sqrt2cdot sqrt{x^3}}= frac{1}{sqrt2} x^{-frac{3}{2}}\\y'=frac{1}{sqrt2}cdot (- frac{3}{2})cdot x^{-frac{5}{2} }=-frac{3}{2sqrt2 cdot sqrt{x^5} } \\2); ; y= frac{ sqrt{x} }{x sqrt[3]{x} } =frac{x^{1/2}}{xcdot x^{1/3}}= frac{x^{1/2}}{x^{4/3}}=x^{ frac{1}{2}-frac{4}{3} }=x^{-frac{5}{6}}\\y'=- frac{5}{6}cdot x^{-frac{11}{6}}=-frac{5}{6cdot sqrt[6]{x^{11}}}$