Jestliže f (x) = sin ^ 3x a g (x) = sqrt (3x-1, co je f '(g (x))?

Jestliže f (x) = sin ^ 3x a g (x) = sqrt (3x-1, co je f '(g (x))?
Anonim

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

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

#D_ (fog) = {## 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 #,

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

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

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