Найти производную от: 1) y=3x lnx-x^32) y=x^2 sinx+2x cosx-2sinx3) y = (3x+2) / (2x+3) 4) y=sqrt (2-3 х^4)

1) y = 3 * x * ln (x) - x^3;

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

2) y = x^2 * sin (x) + 2 * x * cos (x) - 2 * sin (x);

y' = 2 * x * sin (x) + x^2 * cos (x) + 2 * cos (x) + 2 * x * ( - sin (x)) - 2 * cos (x) = x^2 * cos (x);

3) y = (3 * x + 2) / (2 * x + 3);

y' = [3 * (2 * x + 3) - 2 * (2 * x + 3) ] / (2 * x + 3) ^2 = [6 * x + 9 - 4 * x - 6] / (2 * x + 3) ^2 = 1 / (2 * x + 3);

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

у' = (1 / 2) * (2 - 3 * х^4) ^ ( - 1 / 2) * ( - 3 * 4 * x^3) = ( - 6 * x^3) / √ (2 - 3 * x^4).