Найдите производные 1) f(x)=sin x *(cosx-1) 2) f(x)=x^2*ctgx 3) f(x)=cos x (1+sinx) 4) f(x)=x^3*tgx (решение опишите

 1) f(x)\' = (x^3 * sin (2x))’ = (x^3)’ * sin (2x) + x^3 * (sin (2x))’ = (x^3)’ * sin (2x) + x^3 * (2x)’ * (sin (2x))’ = 3x^2 * sin (2x) + x^3 * 2 * cos (2x) = 3x^2sin (2x) + 2x^3cos (2x).

2) f(x)\' = (4tg (x))’ = 4 * (tg (x))’= 4 * (1 / (cos^2 (x)))  = (4 / (cos^2 (x))).

3) f(x)\' = (2sin (x))’ = 2 * (sin (x))’ = 2 * cos (x) = 2cos (x).

4) f(x)\' = (x * cos (2x))’ = (x)’ * cos (2x) + x * (cos (2x))’ = (x)’ * cos (2x) + x * (2x)’ * (sin (2x))’ = 1 * cos (2x) + x * 2 * (-sin (2x)) = cos (2x) - 2xsin (2x).