Απάντηση:
(4x))) ((4)) (2) (2) (2)
(4x)) / sqrt (κούνια (e ^ (4x)) # # (2)
Εξήγηση:
# f (x) = sqrt (κούνια (e ^ (4x))) #
#color (λευκό) (f (x)) = sqrt (g (x)) #
(x) = 1/2 * (g (x)) ^ (- 1/2) * g '(x) #
(x)) = (g '(x) (g (x)) ^ (- 1/2)) / 2 #
#g (x) = κούνια (e ^ (4x)) #
#color (λευκό) (g (x)) = κούνια (h (x)) #
(x) = - h '(x) csc ^ 2 (h (x)) #
# h (x) = e ^ (4x) #
#color (άσπρο) (h (x)) = e ^ (j (x)) #
(x) = j '(x) e ^ (j (x)) #
# j (x) = 4x #
# j '(x) = 4 #
# h '(x) = 4e ^ (4χ) #
(x) = - 4e ^ (4x) csc ^ 2 (e ^ (4x)) #
(4x))) ((4)) (2) (2) (2)
(4x)) / sqrt (κούνια (e ^ (4x)) # # (2)
