Svar:
#f '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (cot (e ^ (4x))) ^ (- 1/2)) / 2 #
#COLOR (hvit) (f (x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4 x))) / sqrt (cot (e ^ (4x)) #
Forklaring:
#f (x) = sqrt (cot (e ^ (4x))) #
#COLOR (hvit) (f (x)) = sqrt (g (x)) #
#f '(x) = 1/2 * (g (x)) ^ (- 1/2) * g' (x) #
#COLOR (hvit) (f (x)) = (g '(x) (g ^ ((x)) - 1/2)) / 2 #
#G (x) = cot (e ^ (4x)) #
#COLOR (hvit) (g (x)) = cot (h (x)) #
#G '(x) = - h' (x) csc ^ 2 (h (x)) #
#h (x) = e ^ (4x) #
#COLOR (hvit) (h (x)) = e ^ (j (x)) #
# t '(x) = j' (x) e ^ (j (x)) #
#J (x) = 4x #
#J '(x) = 4 #
#h '(x) = 4e ^ (4x) #
#G '(x) = - 4e ^ (4x) csc ^ 2 (e ^ (4x)) #
#f '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (cot (e ^ (4x))) ^ (- 1/2)) / 2 #
#COLOR (hvit) (f (x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4 x))) / sqrt (cot (e ^ (4x)) #
