Hvordan skiller du f (x) = 2x * sinx * cosx?

Hvordan skiller du f (x) = 2x * sinx * cosx?
Anonim

Svar:

#f '(x) = 2sinxcosx + 2xcos ^ 2x-2xsin ^ 2x #

Forklaring:

Bruk produktregelen:

# F = GHK # => # F '= g'hk + gh'k + GHK' #

Med:

# G = 2x # => # G '= 2x #

# H = sinx # => # H '= cosx #

# K = cosx # => #k '= - sinx #

Vi har da:

#f '(x) = 2sinxcosx + 2xcos ^ 2x-2xsin ^ 2x #

Svar:

#f '(x) = 2sin (x) cos (x) + 2x (cos ^ 2 (x) -sin ^ 2 (x)) #

Forklaring:

# x 'cdot cos (x)) + 2x cdot (sin (x) cdot cos (x))' # 2 '

# (2x) '= 2 #

# (sin (x) cdot cos (x)) '= sin (x)' cdot cos (x) + sin (x) cdot cos (x) '#

# = cos (x) cdot cos (x) + sin (x) cdot (-sin (x)) #

# = Cos ^ 2 (x) -sin ^ 2 (x) #

#f '(x) = 2sin (x) cos (x) + 2x (cos ^ 2 (x) -sin ^ 2 (x)) #