Найти производные. a) y=ln^5*x^5 б) y=cos x-3/sin 8x в) y=7^x+ctgx г) y = (1/√x + 2) tgx д) y = log2 (tg^4*7x)

1) (y) ' = (ln^5 (x^5)) ' = 5 * ln^4 (x^5) * (x^5) ' = 5 * ln^4 (x^5) * 5 * x^4;

2) (y) ' = (cos^3 (x) - 3 / sin (8x)) ' = 3*cos^2 (x) * (cos (x)) ' - 3 * (-2) * sin^ (-2) (8x) * (sin (8x) ' = - 3 * cos^2 (x) * sin (x) + 48 * sin^2 (8x) * cos (8x).

3) (y) ' = (7^x + ctg (x)) = 7^x * ln (7) - 1 / sin^2 (x);

4) (y) ' = ((1/√x + 2) * tgx) ' = (-3/2) * x^ (-3/2) * tg (x) + (1/√x + 2) * 1 / cos^2 (x).

5) (y) ' = log2 (tg^4 (7x)) = (1 / (tg^4*7x)) * ln (2) * 3 * tg^3 (7x) * 7.