ПРОИЗВОДНАЯ
СРОООЧНОООО
5,6,7,8

5.
f'(x) = cos(3x) * (3x)' = cos(3x) * 3 = 3cos(3x)
при х0=π/12
f'(x0) = 3cos(3* π/12) = 3cos(π/4) = 3* √2/2 = 3√2 / 2

6.
f'(x) = 1/2 * 2x = x
при х0 = 1
f'(x0) = 1

7.
f'(x) = 1/4 * (-4)/(x^5) = -1/x^5
при х0 = 1
f'(x0) = -1/1^5 = -1

8. f'(x) = 2/3 * x√x = 2/3 * x^1 * x^(1/2) = 2/3 * x^(1 + 1/2) = 2/3 * x^(2/2 + 1/2) =

продолжение

= 2/3 * x^(3/2)

f'(x0) = √3