Найти производные: 1. y=lnx+x*e^x 2. y = (x^3+3^x) * tgx 3. y=cosx/x+lnx 4. y=sqrt (x^4+1) 5. y=ln (tgx) 6. y=sin*sqrt (x) / ln (tgx) 7. y=e^4x*cos5x-7x^4

Найдем производные функций:

1. y = ln x + x * e ^ x;

y ' = (ln x + x * e ^ x) ' = 1/x + x ' * e ^ x + (e ^ x) ' * x = 1/x + e ^ x + x * e ^ x;

2. y = (x ^ 3 + 3 ^ x) * tg x;

y ' = (3 * x ^ 2 + 3 ^ x * ln 3) * tg x + (x ^ 3 + 3 ^ x) * 1/cos ^ 2 x;

3. y = cos x/x + ln x;

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

4. y = sqrt (x ^ 4 + 1);

y ' = 1 / (2 * √ (x ^ 4 + 1)) * (x ^ 4 + 1) ' = 1 / (2 * √ (x ^ 4 + 1)) * (4 * x ^ 3);

5. y = ln (tgx);

y ' = 1/tg x * 1/cos ^ 2 x;

6. y = sin sqrt (x) / ln (tg x);

y ' = (cos (√x) * 1 / (2 * x) * ln (tg x) - 1/tg x * 1/cos ^ 2 x * sin (√x)) / (ln ^ 2 (tg x));

7. y = e ^ (4 * x) * cos (5 * x) - 7 * x ^ 4;

y ' = 4 * e ^ (4 * x) * cos (5 * x) - 5 * e ^ (4 * x) * sin (5 * x) - 28 * x ^ 3.