Ako rozlišujete f (x) = sqrt (cote ^ (4x) pomocou pravidla reťazca.?

odpoveď:

# F '(x) = (- 4e ^ (4x) CSC ^ 2 (e ^ (4x)) (lôžko (e ^ (4 x))) ^ (- 1/2)) / 2 #

#COLOR (biely) (f '(x)) = - (2e ^ (4x) CSC ^ 2 (e ^ (4 x))) / sqrt (lôžko (e ^ (4x)) #

# F (x) = sqrt (lôžko (e ^ (4 x))) #

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

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

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

#G (x) = lôžko (e ^ (4x)) #

#COLOR (biely) (g (x)) = lôžko (H (x)) #

#G '(x) = - h' (x) CSC ^ 2 (H (x)) #

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

#COLOR (biely) (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)) (lôžko (e ^ (4 x))) ^ (- 1/2)) / 2 #

#COLOR (biely) (f '(x)) = - (2e ^ (4x) CSC ^ 2 (e ^ (4 x))) / sqrt (lôžko (e ^ (4x)) #