Če je f (x) = sin ^ 3x in g (x) = sqrt (3x-1, kaj je f '(g (x))?

Če je f (x) = sin ^ 3x in g (x) = sqrt (3x-1, kaj je f '(g (x))?
Anonim

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

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

#D_ (megla) = {## 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) #,

  • # (fog) '(x) = f' (g (x)) g '(x) = f' (sqrt (3x-1)) ((3x-1) ') / (2sqrt (3x-1)) #

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

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