Hvordan differentierer du sqrt ((x + 1) / (2x-1))?

Svar:

# - (3 (x + 1)) / (2 (2x-1) ^ 2 sqrt ((x + 1) / (2x-1)) #

Forklaring:

#f (x) = u ^ n #

#f '(x) = n xx (du) / dx xxu ^ (n-1) #

I dette tilfælde:# sqrt ((x + 1) / (2x-1)) = ((x + 1) / (2x-1)) ^ (1/2): #

#n = 1/2, u = (x + 1) / (2x-1) #

2x-1) 2xx ((x + 1) / (2x-1)) ^ (1 / 2x-1) 2-1) #

# = 1 / 2xx (-3) / ((2x-1) ^ 2xx ((x + 1) / (2x-1)) ^ (1 / 2-1)

# = - (3 (x + 1)) / (2 (2x-1) ^ 2 ((x + 1) / (2x-1)) ^

Hvordan differentierer du sqrt (cos (x ^ 2 + 2)) + sqrt (cos ^ 2x + 2)?

(dy) / (dx) = (xsen (x ^ 2 + 2) + sen (x + 2)) / (sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2)) ) / (dx) = 1 / (2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2)) * sen (x ^ 2 + 2) * 2x + 2sen (x + 2) ) / (dx) = (2xsen (x ^ 2 + 2) + 2sen (x + 2)) / (2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) (dx) = (annuller2 (xsen (x ^ 2 + 2) + sen (x + 2))) / (annullér2sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2))) / (dx) = (xsen (x ^ 2 + 2) + sen (x + 2)) / (sqrtcos (x ^ 2 + 2) + sqrt (cos ^ 2 (x + 2)))

Hvordan forenkler du (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Kæmpe matematisk formatering ...> farve (blå) ((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = farve (rød) 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1))) / +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = farve blå) ((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt -1)))) (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = farve / (Sqrt (a-1) -sqrt (a + 1)) / (sqrt (a +

Hvordan differentierer du f (x) = sqrt (ln (1 / sqrt (xe ^ x)) ved hjælp af kædelegemet.?

Bare kæde regel igen og igen. f (x) = e ^ x (1 + x) / 4sqrt (xe ^ x) / (ln (1 / sqrt (xe ^ x)) (xe ^ x) ^ 3)) f (x) = sqrt Ok, det bliver det svært: 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))) (1 / sqrt (xe ^ x)) = = sqrt (xe ^ x) ^ - (1/2)) = = sqrt (xe ^ x) / (2sqrt (ln) (Xe ^ x) ^ - (3/2)) (xe ^ x) '= = sqrt (xe ^ x) / (4sqrt ln (1 / sqrt (xe ^ x)))) (xe ^ x) ^ - (3/2)) (xe ^ x