Kako razlikovati sqrt (cos (x ^ 2 + 2)) + sqrt (cos ^ 2x + 2)?

Odgovor:

# (dy) / (dx) = (xsen (x ^ 2 + 2) + sen (x + 2)) / (sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) #

Obrazloženje:

# (dy) / (dx) = 1 / (2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) * sen (x ^ 2 + 2) * 2x + 2s) #

# (dy) / (dx) = (2xsij (x ^ 2 + 2) + 2sn (x + 2)) / (2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) #

# (dy) / (dx) = (poništi2 (xsen (x ^ 2 + 2) + sen (x + 2))) / (cancel2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) #

# (dy) / (dx) = (xsen (x ^ 2 + 2) + sen (x + 2)) / (sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) #

Kako razlikovati f (x) = sqrt (cote ^ (4x) koristeći lanac pravilo.?

F '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (krevet (e ^ (4x))) ^ (- 1/2)) / 2 boja (bijela) (f') (x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (cot (e ^ (4x)) f (x) = sqrt (cot (e ^ (4x))) boja (bijela) (f (x)) = sqrt (g (x)) f '(x) = 1/2 * (g (x)) ^ (- 1/2) * g' (x) boja (bijela) ) (f '(x)) = (g' (x) (g (x)) ^ (- 1/2)) / 2 g (x) = kolijevka (e ^ (4x)) boja (bijela) (g) (x)) = krevetić (h (x)) g '(x) = - h' (x) csc ^ 2 (h (x)) h (x) = e ^ (4x) boja (bijela) (h ( x)) = e ^ (j (x)) h '(x) = j' (x) e ^ (j (x)) j (x) = 4x j '(x) = 4 h' (x) = 4e ^ (4x) g '(x) = - 4e ^ (4x) csc

Kako razlikovati sqrt ((x + 1) / (2x-1))?

- (3 (x + 1)) / (2 (2x-1) ^ 2 sqrt ((x + 1) / (2x-1)) f (x) = u ^ n f '(x) = n xx ( du) / dx xxu ^ (n-1) U ovom slučaju: sqrt ((x + 1) / (2x-1)) = ((x + 1) / (2x-1)) ^ (1/2): n = 1/2, u = (x + 1) / (2x-1) d / dx = 1/2 xx (1xx (2x-1) - 2xx (x + 1)) / (2x-1) ^ 2 xx ((x + 1) / (2x-1)) ^ (1 / 2-1) = 1 / 2xx (-3) / ((2x-1) ^ 2 xx ((x + 1) / (2x 1)) ^ (1 / 2-1) = - (3 (x + 1)) / (2 (2x-1) ^ 2 ((x + 1) / (2x-1)) ^ (1/2)

Kako razlikovati f (x) = sqrt (ln (1 / sqrt (xe ^ x)) pomoću lančanog pravila.

Samo pravilo lanca iznova i iznova. f '(x) = e ^ x (1 + x) / 4sqrt ((xe ^ x) / (ln (1 / sqrt (xe ^ x)) (xe ^ x) ^ 3)) f (x) = sqrt (ln (1 / sqrt (xe ^ x))) Ok, ovo će biti teško: f '(x) = (sqrt (ln (1 / sqrt (xe ^ x))))' = = 1 / (2sqrt (ln (1 / sqrt (xe ^ x)))) * (ln (1 / sqrt (xe ^ x))) '= = 1 / (2sqrt (ln (1 / sqrt (xe ^ x)))) * 1 / (1 / sqrt (xe ^ x)) (1 / sqrt (xe ^ x)) '= = 1 / (2sqrt (ln (1 / sqrt (xe ^ x)))) * sqrt (xe ^ x) (1 / sqrt (xe ^ x)) '= = sqrt (xe ^ x) / (2sqrt (ln (1 / sqrt (xe ^ x)))) (1 / sqrt (xe ^ x))' = = sqrt (xe ^ x) / (2sqrt (ln (1 / sqrt (xe ^ x)))) ((xe ^ x) ^ - (1/2)