F(x) = 2 arcsin x + arccos вычислите f' (√2 / 2)

f'(x) = 2 / sqrt(1 - x^2) - 1 / sqrt(1 - x^2)

f'(√2 / 2) = 2 / sqrt(1 - ( √2 / 2)^2) - 1 / sqrt(1 - ( √2 / 2)^2) f'(√2 / 2) = 2 / sqrt(1 - 1/2) - 1 / sqrt(1 - 1/2) f'(√2 / 2) = 2 / sqrt(1/2) - 1 / sqrt(1/2) f'(√2 / 2) = 2 / (1 / sqrt(2)) - 1 / (1 / sqrt(2)) f'(√2 / 2) = 2 * sqrt(2) - sqrt(2) f'(√2 / 2) = sqrt(2)