Question

Найти производную....

Answer 1

$2 sqrt[3]{ x^{2} -1} +4 sqrt{ x^{3}-6 x^{2} }=2( x^{2} -1) ^{ frac{1}{3} } +4 sqrt{ x^{3}-6 x^{2} }\\2[( x^{2} -1) ^{ frac{1}{3} }]'+4( sqrt{ x^{3}-6 x^{2} })'=2* frac{1}{3}*( x^{2} -1) ^{- frac{2}{3} }*( x^{2} -1)'+4*$$* frac{1}{2 sqrt{ x^{3}-6 x^{2} } } *( x^{3} -6 x^{2} )'= frac{2}{3}*2x* frac{1}{ sqrt[3]{( x^{2} -1) ^{2} } }+4* frac{3 x^{2} -12x}{2 sqrt{ x^{3}-6 x^{2} } }=$$= frac{4x}{3 sqrt[3]{( x^{2} -1) ^{2} }} + frac{6 x^{2} -24x}{ sqrt{ x^{3}-6 x^{2} } }$