Bagaimana anda membezakan f (x) = sqrt (e ^ cot (x)) menggunakan peraturan rantai?

Jawapan:

f '(x) == -# (sqrt (e ^ cot (x)). csc ^ 2 (x)) / 2 #

Penjelasan:

#f (x) = sqrt (e ^ cot (x)) #

Untuk mencari derivatif f (x), kita perlu menggunakan peraturan rantai.

#color (red) "rantai: f (g (x)) '= f' (g (x)) g '(x)" #

Biarkan #u (x) = cot (x) => u '(x) = - csc ^ 2 (x) #

dan # g (x) = e ^ (x) => g '(x) = e ^ (x).g' (u (x)) = e ^ cot (x)

(x) => (x) = 1 / (2sqrt (x)) => f '(g (u (x))) = 1 / (2sqrt (e ^)) #

# d / dx (f (g (u (x))) = f '(g (u (x))) g' (u (x)

=# 1 / (sqrt (e ^ cot (x))) e ^ cot (x).- cos ^ 2 (x) #

=# (- e ^ cot (x) csc ^ 2x) / sqrt (e ^ cot (x)) #

#color (biru) "membatalkan e ^ cot (x) dengan sqrt (e ^ cot (x)) dalam penyebut" #

=-# (sqrt (e ^ cot (x)). csc ^ 2 (x)) / 2 #

Bagaimana anda membezakan f (x) = sqrt (cote ^ (4x) menggunakan peraturan rantai.?

(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x)) (cot (e ^ (4x))) ^ (- 1/2) (x) = sqrt (cot (e ^ (4x)) = - (2e ^ (4x) csc ^ (x) = f (x)) = sqrt (g (x)) f '(x) = 1/2 * (g (x)) ^ (- 1/2) (g '(x)) = (g' (x) (g (x)) ^ (- 1/2)) / 2 g (x) = cot (e ^ (4x) (x) = cot (h (x)) g '(x) = - h' (x) csc ^ 2 (h (x) (x) = h (x) = j '(x) e ^ (j (x) = j (x) = 4x j' (x) = 4 h ' (X) = - 4e ^ (4x) csc ^ 2 (e ^ (4x)) f '(x) = (- 4e ^ (4x) csc ^ 2 (e ^ (4x) (cot (e ^ (4x))) ^ (- 1/2)) / 2 warna (putih) (f '(x)) = - (2e ^ (4x) csc ^ 2 (e ^ (4x))) / sqrt (cot (e ^ (4x))

Bagaimana anda membezakan f (x) = sqrt (ln (x ^ 2 + 3) menggunakan peraturan rantai.?

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

Bagaimana anda membezakan f (x) = sqrt (ln (1 / sqrt (xe ^ x)) menggunakan peraturan rantai.?

Sekadar aturan rantai lagi dan lagi. 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)))) '= = 1 / (2sqrt (ln (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) (xe ^ x) / (2sqrt (ln (1 / sqrt (xe ^ x)))) ((xe ^ x) ^ - (1/2)) '= = sqrt (xe ^ x) / (2sqrt (ln (1 / sqrt (xe ^ x))) (- 1/2) ((xe ^ x) ^ - (3/2)) (xe ^ x) '= = sqrt (xe ^ x) / (4sqrt ( ln (1 / sqrt (xe ^ x)))) (xe ^ x) ^ - (3/2)) (xe ^ x) '= = sqrt (xe ^ x) / (4sqrt (ln (1