Ak f (x) = sin ^ 3x a g (x) = sqrt (3x-1, čo je f '(g (x))?

Ak f (x) = sin ^ 3x a g (x) = sqrt (3x-1, čo je f '(g (x))?
Anonim

# F (x) = sin ^ 3x #, # D_f = RR #

#G (x) = sqrt (3x-1) #, # Dg = 1/3, + oo) #

#D_ (hmla) = {## # AAX# V ##RR: ##X## V ## # D_g, #G (x) ## V ##D_f} #

#X> = 1/3 #, #sqrt (3x-1) ## V ## RR # #-># #X## V ## 1/3, + oo) #

# # AAX# V ## 1/3, + oo) #,

  • # (Hmla) '(x) = f (G (x)), g' (x) = f '(sqrt (3 x-1)) ((3 x-1) ") / (2sqrt (3x-1)) #

# F '(x) = 3sin ^ 2x (sinx)' = 3sin ^ 2xcosx #

tak # (Hmla) '(x) = sin ^ 2 (sqrt (3 x-1)) cos (sqrt (3 x-1)) * 9 / (2sqrt (3x-1)) #