체인 규칙을 사용하여 f (x) = sqrt (cote ^ (4x))를 어떻게 구별합니까?

대답:

(4x)) ^ (- 1/2)) / 2 # (4e) (4x)

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

설명:

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

#color (흰색) (f (x)) = sqrt (g (x)) #

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

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

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

#color (흰색) (g (x)) = cot (h (x)) #

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

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

#color (흰색) (h (x)) = e ^ (j (x)) #

(x) = j '(x) e ^ (j (x)) #h'(x)

#j (x) = 4x #

#j '(x) = 4 #

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

# g '(x) = - 4e ^ (4x) csc ^ 2 (e ^ (4x)) #

(4x)) ^ (- 1/2)) / 2 # (4e) (4x)

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