Com es diferencien f (x) = 2x * sinx * cosx?

Resposta:

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

Explicació:

Utilitzeu la regla del producte:

# f = ghk # => # f '= g'hk + gh'k + ghk' #

Amb:

# g = 2x # => # g '= 2x #

# h = sinx # => # h '= cosx #

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

Llavors tenim:

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

Resposta:

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

Explicació:

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

# (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) = 2in (x) cos (x) + 2x (cos ^ 2 (x) -sin ^ 2 (x)) #