Als f (x) = sin ^ 3x en g (x) = sqrt (3x-1, wat is f '(g (x))?

Als f (x) = sin ^ 3x en g (x) = sqrt (3x-1, wat is f '(g (x))?
Anonim

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

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

#D_ (mist) = {## AAx ##in##RR: ##X##in## D_g #, #G (x) ##in##D_f} #

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

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

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

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

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