체인 규칙을 사용하여 f (x) = sqrt (ln (x ^ 2 + 3))를 어떻게 구별합니까?

대답:

(x ^ 2 + 3) = (x ^ 2 + 3) = x / (x ^ 2 + 3) (ln (x) ^ 2 + 3)) ^ (1/2)) = x / (x ^ 2 + 3) sqrt (ln (x ^ 2 + 3)

설명:

우리는 주어진다:

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

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

(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 #

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