Wat is de afgeleide van de functie f (x) = ln (ln ((x + 4) / ln (x ^ 2 + 4)?

Antwoord:

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

Uitleg:

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

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

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