Jeśli f (x) = sin ^ 3x oraz g (x) = sqrt (3x-1, co to jest f '(g (x))?

Jeśli f (x) = sin ^ 3x oraz g (x) = sqrt (3x-1, co to jest f '(g (x))?
Anonim

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

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

#D_ (fog) = {## AAx ##w##RR: ## x ##w## D_g #, #g (x) ##w##D_f} #

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

# AAx ##w## 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 #

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