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)

Question

Accepted Answer

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.

Найти производные. a) y=ln^5x^5 б) y=cos x-3/sin 8x в) y=7^x+ctgx г) y=(1/√x +2)tgx д) y= log2(tg^47x)