Найти значение производной в т. x0: f (x) = 7x^2-56x+8, x0=4. f (x) = 4x / (x^2+4), x0=0 Найдите производную функции: f (x) = 2^ (5x+3). f (x) = e^2x + 5x

1) f' (x) = (7x^2 - 56x + 6) ' = 14x - 56.

f' (4) = 14 * 4 - 56 = 56 - 56 = 0.

2) f' (x) = ((4x) ' * (x^2 + 4) - 4x * (x^2 + 4) ') / (x^2 + 4) ^2 = (4 (x^2 + 4) -

4x * 2x)) / (x^2 + 4) ^2 = (4 - 4x) / (x^2 + 4) ^2.

f' (0) = (4 - 0) / (0 + 4) ^2 = 4/16 = 1/4.

3) f' (x) = (2^ (5x + 3)) ' = 2^ (5x + 3) * ln (2) * (5x + 3) ' = 2^ (5x + 3) * ln (2) * 5.