F(x) = 5 arcsin x + 2 arccos x вычислите f'(1/2)

f(x) = 5 arcsin x + 2 arccos x, вычислим f'(1/2).

f'(x) = 5 * 1/sqrt(1-x^2) - 2 * (-1/sqrt(1-x^2)), где x = 1/2.

f'(1/2) = 5 * 1/sqrt(1-(1/2)^2) - 2 * (-1/sqrt(1-(1/2)^2))
f'(1/2) = 5 * 1/sqrt(1-1/4) + 2 * 1/sqrt(1-1/4)
f'(1/2) = 5 * 1/sqrt(3/4) + 2 * 1/sqrt(3/4)
f'(1/2) = 5 * 1/(sqrt(3)/2) + 2 * 1/(sqrt(3)/2)
f'(1/2) = 10/sqrt(3) + 4/sqrt(3)
f'(1/2) = 14/sqrt(3)