Ako je f (x) = sin ^ 3x i g (x) = sqrt (3x-1, što je f '(g (x))?

Ako je f (x) = sin ^ 3x i g (x) = sqrt (3x-1, što je f '(g (x))?
Anonim

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

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

#D_ (magla) = {## As ##u##RR: ##x##u## D_g #, #G (x) *#u##D_f} #

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

# As ##u## 1/3, + oo) #,

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

#F "(x) = 3sin ^ 2x (sinx) = 3sin ^ 2xcosx #

tako # (Magla) (x) = sin ^ 2 (sqrt (3 x-1)) cos (sqrt (3 x-1)) * 9 / (2sqrt (3 x-1)) *