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} } }$