Производные y=tg3x/x^6; y=x^sinx;

1) y = tg (3x) / x^6;

y' = {1 / [cos (3x) ]^2 * 3 * x^6 - tg (3x) * 6 * x^5} / x^12 = {3 * x / [cos (3x) ]^2 - 6 * tg (3x) } / x^7 = {3 * x - 6 * sin (3x) * cos (3x) } / {x^7 * [cos (3x) ]^2} = 3 * [x - sin (6x] / {x^7 * [cos (3x) ]^2}.

2) y = x^sin (x);

ln (y) = ln (x^sin (x));

ln (y) = sin (x) * ln (x);

1 / y * y' = cos (x) * ln (x) + sin (x) * 1/x;

y' = y * [cos (x) * ln (x) + sin (x) / x] = x^sin (x) * [cos (x) * ln (x) + sin (x) / x].