Jaká je derivace f (x) = sin (cos (tanx))?

Jaká je derivace f (x) = sin (cos (tanx))?
Anonim

Odpovědět:

#f '(x) = - sec ^ 2xsin (tanx) cos (cos (tanx)) #

Vysvětlení:

#f (x) = sin (g (x)) #

#f '(x) = g' (x) cos (g (x)) #

#g (x) = cos (h (x)) #

#g '(x) = - h' (x) sin (h (x)) #

#h (x) = tan (x) #

#h '(x) = sec ^ 2x #

#g '(x) = - sec ^ 2xsin (tanx) #

#g (x) = cos (tanx) #

#f '(x) = - sec ^ 2xsin (tanx) cos (cos (tanx)) #