Вычислить производную 1. (X*е^х)' 2. (X^3*lnx)' 3. (Sin5x)' 4. ((2x-3)^3)' 5. (2x/lnx)'

1) (x * e^x)\' = (x)\' * e^x + x * (e^x)\' = e^x + e^x * x = (1 + x ) * e^x;

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

3) (sin(5x))\' = 5 * cos(5x);

4) ((2x - 3)^3)\' = 3 * (2x - 3)^2 * (2x - 3)\' = 6 * (2x - 3)^2;

5) (2x/ln(x))\' = (2 * ln(x) - 2x * (1/x)) / (ln(x))^2.