Question

Найти производную

y=ln² cos³ (4x-1)

Answer 1

$displaystyle y=ln^2cos^3(4x-1)\\y'=2lncos^3(4x-1)cdot(lncos^3(4x-1))'=frac{2lncos^3(4x-1)}{cos^3(4x-1)}cdot\\\cdot (cos^3(4x-1))'=frac{2lncos^3(4x-1)}{cos^3(4x-1)}cdot3cos^2(4x-1)cdot(cos(4x-1))'=\\\=frac{6lncos^3(4x-1)}{cos(4x-1)}cdot(-sin(4x-1))cdot (4x-1)'=-frac{sin(4x-1)}{cos(4x-1)}cdot\\\cdot 6lncos^3(4x-1)cdot4=boxed{-24tg(4x-1)cdotlncos^3(4x-1)}$

Answer 2

по условию cos^3

Answer 3

и аргумент 4х-1

Answer 4

Спасибо! Поправил