Найти производную функции: 1) f (x) = (4-3x) ^7 2) f (x) = x^3lnx 3) f (x) = cosx-lnx

Вычислим производные функций:

1) f (x) = (4 - 3 * x) ^7;

f ' (x) = ((4 - 3 * x) ^7) ' = 7 * (4 - 3 * x) ^6 * (4 - 3 * x) ' = 7 * (4 - 3 * x) ^6 * (4 ' - 3 * x ') = 7 * (4 - 3 * x) ^6 * (0 - 3 * 1) = 7 * (4 - 3 * x) ^6 * (-3) = - 3 * 7 * (4 - 3 * x) ^6 = - 21 * (4 - 3 * x) ^6;

2) f (x) = x^3 * ln x;

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

3) f (x) = cos x - ln x;

f ' (x) ' = (cos x - ln x) ' = cos ' x - ln ' x = - sin x - 1/x.