F (x) = 2sin 5x F (x) = sin^2 x F (x) = ln * sin x F (x) = cos^100 2x

(F(x))\' = (2sin(5x))\' = 2 * (5x)\' * cos(5x) = 10 * cos(5x);

(F(x))\' = (sin^2(x))\' = 2 * sin(x) * ((sin(x))\' = 2 * sin(x) * ( -cos(x));

(F(x))\' = (ln(sin(x)))\' = 1/sin(x) * (sin(x))\' = - cos(x) / sin(x) = -ctg(x);

(F(x))\' = (cos^100(2x) = 100 * cos^99 (2x) * (cos(2x))\' = 100 * cos^99(2x) * 2 * (- sin(x)).