Odgovor:
#F "(x) = (x (ln (x ^ 2 + 3)) ^ (- 1/2)) / (x ^ 2 + 3) = x / ((x ^ 2 + 3) (ln (x ^ 2 + 3)) ^ (1/2)) = x / ((x ^ 2 + 3) sqrt (ln (x ^ 2 + 3))) *
Obrazloženje:
Dobili smo:
# Y = (ln (x ^ 2 + 3)) ^ (1/2) #
# Y = 1 / 2x (ln (x ^ 2 + 3)) ^ (1 / 2-1) + d / dx ln (x ^ 2 + 3) #
#Y '= (ln (x ^ 2 + 3)) ^ (- 1/2) / 2 x d / dx ln (x ^ 2 + 3) #
# D / dx ln (x ^ 2 + 3) = (d / dx x ^ 2 + 3) / (x ^ 2 + 3) *
# D / dx x ^ 2 + 3 = 2x #
#Y '= (ln (x ^ 2 + 3)) ^ (- 1/2) / 2 x (2 x) / (x ^ 2 + 3) = (x (ln (x ^ 2 + 3)) ^ (-1/2)) / (x ^ 2 + 3) = x / ((x ^ 2 + 3) (ln (x ^ 2 + 3)) ^ (1/2)) = x / ((x ^ 2 + 3) sqrt (ln (x ^ 2 + 3))) *
