Wie lautet die Ableitung der Funktion f (x) = ln (ln ((x + 4) / ln (x ^ 2 + 4))?

Wie lautet die Ableitung der Funktion f (x) = ln (ln ((x + 4) / ln (x ^ 2 + 4))?
Anonim

Antworten:

#f '(x) = (1 / (In ((x + 4) / (In (x ^ 2 + 4))))) ((1) / ((x + 4))). (((x ^ 2 + 4) (In (x ^ 2 + 4)) - (2x ^ 2 + 4x)) / ((x ^ 2 + 4) (In (x ^ 2 + 4))))

Erläuterung:

#f '(x) = (1 / (In ((x + 4) / (In (x ^ 2 + 4))))) (1 / ((x + 4)) / (In (x ^ 2 + 4))))). (((1) (In (x ^ 2 + 4)) - (x + 4) (1) / ((x ^ 2 + 4)) (2x)) / ((ln (x ^) 2 + 4))) ^ 2) #

#f '(x) = (1 / (ln ((x + 4) / (ln (x ^ 2 + 4))))) (ln (x ^ 2 + 4) / ((x + 4))) ((In (x ^ 2 + 4) - (2x ^ 2 + 4x) / ((x ^ 2 + 4))) / ((ln (x ^ 2 + 4))) ^ 2) #

#f '(x) = (1 / (ln ((x + 4) / (ln (x ^ 2 + 4)))))) (Löschen (ln (x ^ 2 + 4)) / ((x + 4)))). (((x ^ 2 + 4) (ln (x ^ 2 + 4)) - (2x ^ 2 + 4x)) / ((x ^ 2 + 4) (ln (x ^ 2 + 4)) ^ abbrechen (2))) #

#f '(x) = (1 / (In ((x + 4) / (In (x ^ 2 + 4))))) ((1) / ((x + 4))). (((x ^ 2 + 4) (In (x ^ 2 + 4)) - (2x ^ 2 + 4x)) / ((x ^ 2 + 4) (In (x ^ 2 + 4))))