Bagaimana anda membezakan f (x) = tan (e ^ ((lnx-2) ^ 2)) menggunakan peraturan rantai.

Jawapan:

# ((2sec ^ 2 (e ^ ((ln (x) -2) ^ 2)) e ^ ((ln (x) -2) ^ 2) (lnx-2)) / x) #

Penjelasan:

# d / dx (tan (e ^ ((ln (x) -2) ^ 2))) = sec ^ 2 (e ^ ((ln (x) -2) ^ 2) ^ ((ln (x) -2) ^ 2)) #

=# sec ^ 2 (e ^ ((ln (x) -2) ^ 2)) e ^ (((ln (x) -2)) ^ 2) * d / dx (ln (x) #

=# sec ^ 2 (e ^ ((ln (x) -2) ^ 2)) e ^ (((ln (x) -2)) ^ 2) 2 (lnx-2) * d / dx (lnx-2) #

=# (sec ^ 2 (e ^ ((ln (x) -2) ^ 2)) e ^ (((ln (x) -2)) ^ 2) 2 (lnx-2) * 1 / x) #

=# ((2sec ^ 2 (e ^ ((ln (x) -2) ^ 2)) e ^ ((ln (x) -2) ^ 2) (lnx-2)) / x) #

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 menggunakan peraturan rantai untuk membezakan f (x) = sin (tan (5 + 1 / x) -7x)?

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