Hvordan differentierer du f (x) = sqrt (cote ^ (4x) ved hjælp af kædelegemet.?

Svar:

#F '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (barneseng (e ^ (4x))) ^ (- 1/2)) / 2 #

#COLOR (hvid) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (barneseng (e ^ (4x)) #

#F (x) = sqrt (barneseng (e ^ (4x))) #

#COLOR (hvid) (f (x)) = sqrt (g (x)) #

#F '(x) = 1/2 * (g (x)) ^ (- 1/2) * g' (x) #

#COLOR (hvid) (f '(x)) = (g' (x) (g (x)) ^ (- 1/2)) / 2 #

#g (x) = barneseng (e ^ (4x)) #

#COLOR (hvid) (g (x)) = barneseng (h (x)) #

#g '(x) = - h' (x) csc ^ 2 (h (x)) #

#h (x) = e ^ (4x) #

#COLOR (hvid) (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)) (barneseng (e ^ (4x))) ^ (- 1/2)) / 2 #

#COLOR (hvid) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (barneseng (e ^ (4x)) #