Question

Найти производную сложной функции:
$y = 5 cos (sin(2x^{6}-2))$

Answer 1

Ответ:

$y=5\, cos(sin(2x^6-2))\ \ \ ,\ \ \ \ (cosu)'=-sinu\cdot u'\ ,\ u=sin(2x^6-2)\\\\\\y'=-5sin(sin(2x^6-2))\cdot (sin(2x^6-2))'=\Big[\ (sinu)'=cosu\cdot u'\ ,\ u=2x^6-2\ \Big]=\\\\=-5sin(sin(2x^6-2))\cdot cos(2x^6-2)\cdot (2x^6-2)'=\\\\=-5sin(sin(2x^6-2))\cdot cos(2x^6-2)\cdot 12x$