Question

Найти производную функции y=tg⁵(3x⁴-13)

Answer 1

$y'=( tg^{5}(3 x^{4}-13 ) )'=5* tg^{4} (3 x^{4}-13 )*(tg(3 x^{4}-13 ))'=$
$=5 tg^{4}(3 x^{4}-13 )* \frac{1}{ cos^{2}(3 x^{4}-13 ) } *(3 x^{4}-13 )'=$
$=5 tg^{4} (3 x^{4}-13 )* \frac{1}{cos^{2} (3 x^{4}-13 )} *12 x^{3}= \frac{60 x^{3}* tg^{4} (3 x^{4}-13 ) }{ cos^{2} (3 x^{4}-13 )}$