Question

используя таблицу производных найдите f(x)=2sinx-2cosx-tgx. x0=π/3
f(x)=√(2x-1) x0=1

Answer 1

f(x) = 2sinx - 2cosx - tgx
f'(x) = 2cosx + 2sinx - 1/cos²x
f'(π/3) = 2cos(π/3) + 2sin(π/3) - 1/cos²(π/3) = 2·1/2 + 2·√3/2 - 1/(1/4) = 1 + √3 - 4 = -3 + √3

f(x) = √(2x - 1)
f'(x) = 2/2√(2x - 1) = 1/√(2x - 1)
f'(1) = 1/√(2·1 - 1) = 1/√1 = 1