Come si differenzia f (x) = sqrt (ln (x ^ 2 + 3) usando la regola della catena.?

Risposta:

#f '(x) = (x (ln (x ^ 2 + 3)) ^ (- 1/2)) / (x ^ 2 + 3) = x / ((x ^ 2 + 3) (ln (x ^ 2 + 3)) ^ (1/2)) = x / ((x ^ 2 + 3) sqrt (ln (x ^ 2 + 3))) #

Spiegazione:

Ci viene dato:

# Y = (ln (x ^ 2 + 3)) ^ (1/2) #

# Y '= 1/2 * (ln (x ^ 2 + 3)) ^ (1 / 2-1) * d / dx ln (x ^ 2 + 3) #

#y '= (ln (x ^ 2 + 3)) ^ (- 1/2) / 2 * d / dx ln (x ^ 2 + 3) #

# D / dx ln (x ^ 2 + 3) = (d / dx x ^ 2 + 3) / (x ^ 2 + 3) #

# D / dx x ^ 2 + 3 = 2x #

#y '= (ln (x ^ 2 + 3)) ^ (- 1/2) / 2 * (2x) / (x ^ 2 + 3) = (x (ln (x ^ 2 + 3)) ^ (-1/2)) / (x ^ 2 + 3) = x / ((x ^ 2 + 3) (ln (x ^ 2 + 3)) ^ (1/2)) = x / ((x ^ 2 3) sqrt (ln (x ^ 2 + 3))) #