Kung f (x) = sin ^ 3x at g (x) = sqrt (3x-1, ano ang f '(g (x))?

Kung f (x) = sin ^ 3x at g (x) = sqrt (3x-1, ano ang f '(g (x))?
Anonim

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

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

#D_ (fog) = {## AAx ##sa##RR: ## x ##sa## D #, #g (x) ##sa##D_f} #

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

# AAx ##sa## 1/3, + oo) #,

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

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

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