Question

Найти производную функции
$y = (6^{sin6x} - cos^{3} 6x)^3$

Answer 1

Ответ:

$y = {( {6}^{ \sin(6x) } - \cos^{3} (6x) )}^{3}$

$y '= 3 {( {6}^{ \sin(6x) } - \cos^{3} (6x) }^{2} ) \times ( {6}^{ \sin(6x) } - \cos^{3} (6x))' = \\ = 3 {( {6}^{ \sin(6x) } - \cos ^{3} (6x)) }^{2} \times ( ln(6) \times {6}^{ \sin(6x ) } \times 6 \cos(6x) - 3 \cos ^{2} (6x) \times ( - \sin(6x) ) \times 6) = \\ = 3 {( {6}^{ \sin(6x) } - \cos ^{3} (6x)) }^{2} \times( 6ln(6) \cos(6x) \times {6}^{ \sin(6x) } + 18 \sin(6x) { \cos }^{2} (6x))$