Question

Найти производную
$y=ln \sqrt[3]{( \frac{1-3x}{1+3x})^{2} }$

Answer 1

y = ln ((1 -3x)/(1 +3x))^2/3 = 2/3 ln ((1 -3x)/(1 +3x))
y' = 2/3*1/ ((1 -3x)/(1 +3x)) *((1 -3x)/(1 +3x))' =
=  2/3*1/ ((1 -3x)/(1 +3x)) * (-3(1+3x) - 3(1 -3x))/(1 +3x)² =
= 2/3*1/ ((1 -3x)/(1 +3x)) * (-3 -9x -3 +9x)/(1 + 3x)² =
= - 2/3*1/ ((1 -3x)/(1 +3x)) * 6/(1 +3x)²