Question

найти производную сложной функции
y=ln($sqrt[6]{ frac{1-8 x^{2} }{7x^{3}-4 } }$) + arcsin$frac{5}{1-3x}$

Answer 1

$y=lnsqrt[6]{frac{1-8x^2}{7x^3-4}}+arcsinfrac{5}{1-3x}\\y'=sqrt[6]{frac{7x^3-4}{1-8x^2}}cdot frac{1}{6}cdot (frac{1-8x^2}{7x^3-4})^{-frac{5}{6}}cdot frac{-16x(7x^3-4)-(1-8x^2)cdot 21x^2}{(7x^3-4)^2}+\\+frac{1}{sqrt{1-(frac{5}{1-3x})^2}}cdot frac{-5cdot (-3)}{(1-3x)^2}$