Question

Найти производную y=ln² cos³ (4x-1)

Answer 1

$\displaystyle y=\ln^2\cos^3(4x-1)\\\\y'=2\ln\cos^3(4x-1)\cdot(\ln\cos^3(4x-1))'=\frac{2\ln\cos^3(4x-1)}{\cos^3(4x-1)}\cdot\\\\\\\cdot (\cos^3(4x-1))'=\frac{2\ln\cos^3(4x-1)}{\cos^3(4x-1)}\cdot3\cos^2(4x-1)\cdot(\cos(4x-1))'=\\\\\\=\frac{6\ln\cos^3(4x-1)}{\cos(4x-1)}\cdot(-\sin(4x-1))\cdot (4x-1)'=-\frac{\sin(4x-1)}{\cos(4x-1)}\cdot\\\\\\\cdot 6\ln\cos^3(4x-1)\cdot4=\boxed{-24tg(4x-1)\cdot\ln\cos^3(4x-1)}$