תשובה:
# ('x) = (4x) cx ^ 2 (e ^ (4x)) (c (e ^ (4x)) ^ (- 1/2)) / 2 #
# (x) (= x) (= x) (= x) (= x) (= x)
הסבר:
#f (x) = sqrt (cot (e ^ (4x)) #
#color (לבן) (f (x)) = sqrt (g (x)) #
# (') = 1/2 * (g (x)) ^ (- 1/2) * g' (x) #
# (x) (x (x)) (x ()) ()
#g (x) = cot (e ^ (4x)) #
#color (לבן) (g (x)) = cot (h (x)) #
# g '(x) = - h' (x) csc ^ 2 (h (x)) #
#h (x) = e ^ (4x) #
#color (לבן) (h (x)) = e ^ (j (x)) #
#h '(x) = j' (x) e ^ (j (x)) #
#j (x) = 4x #
#j '(x) = 4 #
#h '(x) = 4e ^ (4x) #
# # '(x) = - 4e ^ (4x) csc ^ 2 (e ^ (4x)) #
# ('x) = (4x) cx ^ 2 (e ^ (4x)) (c (e ^ (4x)) ^ (- 1/2)) / 2 #
# (x) (= x) (= x) (= x) (= x) (= x)
