1) f'(x) = -2x cos(x²)При x₀=0: f'(0) = 0
2) f'(x) = 2x sin(x²)При x₀=0: f'(0) = 0
3) f'(x) = -9tg²(2-3x) sec²(2-3x)При x₀=0: f'(0) = 0
4) f'(x) = -16ctg³(2x-1) csc²(2x-1)При x₀=0: f'(0) = 0
5) f'(x) = cos(x³+x-π/4)(3x²+1)При x₀=0: f'(0) = cos(-π/4) = -√2/2
6) f'(x) = 2tg(x²+π/6)(2x)При x₀=0: f'(0) = 0
Итак, найдены значения производных функций в точке x₀=0.
1) f'(x) = -2x cos(x²)
При x₀=0: f'(0) = 0
2) f'(x) = 2x sin(x²)
При x₀=0: f'(0) = 0
3) f'(x) = -9tg²(2-3x) sec²(2-3x)
При x₀=0: f'(0) = 0
4) f'(x) = -16ctg³(2x-1) csc²(2x-1)
При x₀=0: f'(0) = 0
5) f'(x) = cos(x³+x-π/4)(3x²+1)
При x₀=0: f'(0) = cos(-π/4) = -√2/2
6) f'(x) = 2tg(x²+π/6)(2x)
При x₀=0: f'(0) = 0
Итак, найдены значения производных функций в точке x₀=0.