Hva er derivatet av funksjonen f (x) = ln (ln ((x + 4) / ln (x ^ 2 + 4)?

Hva er derivatet av funksjonen f (x) = ln (ln ((x + 4) / ln (x ^ 2 + 4)?
Anonim

Svar:

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

Forklaring:

(1 x (4) / (ln (x ^ 2 + 4)))) (1 / ((x + 4) / (ln (x ^ 2 + 4)))) (((1) (ln (x ^ 2 + 4)) -. (x + 4) (1) / ((x ^ 2 + 4)) (2 x)) / ((ln (x ^ 2 + 4))) ^ 2) #

(ln (x + 4) / (ln (x ^ 2 + 4)))) (ln (x ^ 2 + 4) / ((x + 4))). ((ln (x ^ 2 + 4) - (2x ^ 2 + 4x) / ((x ^ 2 + 4))) / ((ln (x ^ 2 + 4))) ^ 2) #

(ln (x ^ 2)))))) (((x ^ 2 + 4) (ln (x ^ 2 + 4)) -. (2 x ^ 2 + 4x)) / ((x ^ 2 + 4) (ln (x ^ 2 + 4)) ^ avbryt (2))) #

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