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.