Jika f (x) = sin ^ 3x dan g (x) = sqrt (3x-1, apa itu f '(g (x))?

Jika f (x) = sin ^ 3x dan g (x) = sqrt (3x-1, apa itu f '(g (x))?
Anonim

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

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

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

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

# AAx ##di## 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 #

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