Cum diferentiati f (x) = sqrt (cote ^ (4x) folosind regula lantului?

Răspuns:

#f '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (pătuț (e ^ (4x))) ^ (- 1/2)) / 2 #

#color (alb) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (patut (e ^ (4x)) #

#f (x) = sqrt (patut (e ^ (4x))) #

#color (alb) (f (x)) = sqrt (g (x)) #

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

#color (alb) (f '(x)) = (g' (x), (g (x)) ^ (- 1/2)) / 2 #

#G (x) = patut (e ^ (4x)) #

#color (alb) (g (x)) = patut (h (x)) #

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

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

#color (alb) (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)) (pătuț (e ^ (4x))) ^ (- 1/2)) / 2 #

#color (alb) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (patut (e ^ (4x)) #