Antwoord:
#f '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (cot (e ^ (4x))) ^ (- 02/01)) / 2 #
#color (wit) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (kinderbed (e ^ (4x)) #
Uitleg:
#f (x) = sqrt (kinderbed (e ^ (4x))) #
#color (wit) (f (x)) = sqrt (g (x)) #
#f '(x) = 1/2 * (g (x)) ^ (- 02/01) * g' (x) #
#color (wit) (f '(x)) = (g' (x) (g (x)) ^ (- 02/01)) / 2 #
#G (x) = kinderbed (e ^ (4x)) #
#color (wit) (g (x)) = kinderbed (h (x)) #
#G '(x) = - h' (x) csc ^ 2 (h (x)) #
#h (x) = e ^ (4x) #
#color (wit) (h (x)) = e ^ (j (x)) #
#h '(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))) ^ (- 02/01)) / 2 #
#color (wit) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (kinderbed (e ^ (4x)) #
