Question

Найти производную заданной функции!
y=8(lncos5x)^7

Answer 1

$y = 8 ln {}^{7} ( \cos(5x))\\ y' = 8( ln( \cos(5x) ) )' ({(g)}^{7}) ' = 8( \cos(5x) )'( ln(h)) '7g {}^{6} = \\ = - 280 \sin(5x) \frac{1}{ \cos(5x) } \times ln {}^{6} ( \cos(5x) ) = \\ = - 280 \tan(5x) ln {}^{6} ( \cos(5x) )$

Answer 2

y'=(8(lncos5x)⁷)'=8*7(lncos5x)⁶*(lncos5x)'=56(lncos5x)⁶*(1/cos5x)*(cos5x)'=

56(lncos5x)⁶*(1/cos5x)*(-sin5x)*(5x)'=

56(lncos5x)⁶*(1/cos5x)*(-sin5x)*(5)=-280(tg5x)*(lncos5x)⁶