Найти производную функции номер 22 сделаю лучшим ответом

y' = (√(e^(-x) + x^2) * tg^6(7x) + tg(3))'
y' = (√(e^(-x) + x^2) * tg^6(7x))' + (tg(3))'

(tg(3))' = 0

(√(e^(-x) + x^2) * tg^6(7x))' = (√(e^(-x) + x^2))' * tg^6(7x) + √(e^(-x) + x^2) * (tg^6(7x))'

(√(e^(-x) + x^2))' = ((e^(-x) + x^2)^(1/2))'
= (1/2) * (e^(-x) + x^2)^(-1/2) * (e^(-x) + x^2)'
= (1 / (2 * √(e^(-x) + x^2))) * (-e^(-x) + 2x)
= (2x - e^(-x)) / (2 * √(e^(-x) + x^2))

(tg^6(7x))' = ((tg(7x))^6)'
= 6 * (tg(7x))^5 * (tg(7x))'
= 6 * tg^5(7x) * (sec^2(7x) * (7x)')
= 6 * tg^5(7x) * sec^2(7x) * 7
= 42 * tg^5(7x) * sec^2(7x)

(√(e^(-x) + x^2) * tg^6(7x))' = [(2x - e^(-x)) / (2 * √(e^(-x) + x^2))] * tg^6(7x) + √(e^(-x) + x^2) * 42 * tg^5(7x) * sec^2(7x)

y' = [(2x - e^(-x)) * tg^6(7x)] / [2 * √(e^(-x) + x^2)] + 42 * √(e^(-x) + x^2) * tg^5(7x) * sec^2(7x) + 0

y' = ( (2x - e^(-x)) * tg^6(7x) ) / ( 2 * √(e^(-x) + x^2) ) + 42 * √(e^(-x) + x^2) * tg^5(7x) * sec^2(7x)