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Bagaimana Anda membedakan f (x) = sqrt (cote ^ (4x) menggunakan aturan rantai.?
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)) f (x) = sqrt (cot (e ^ (4x)))) warna (putih) (f (x)) = sqrt (g (x)) f '(x) = 1/2 * (g (x)) ^ (- 1/2) * g' (x) warna (putih) ) (f '(x)) = (g' (x) (g (x)) ^ (- 1/2)) / 2 g (x) = warna cot (e ^ (4x)) (putih) (g) (x)) = cot (h (x)) g '(x) = - h' (x) csc ^ 2 (h (x)) h (x) = e ^ (4x) warna (putih) (h ( x)) = e ^ (j (x)) h '(x) = j' (x) e ^ (j (x)) j (x) = 4x j '(x) = 4 h' (x) = 4e ^ (4x) g '(x) = - 4e ^ (4x) csc ^ 2 (e ^ (4x))
Bagaimana Anda membedakan f (x) = sqrt (ln (x ^ 2 + 3) menggunakan aturan rantai.?
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))) Kita diberi: 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))))
Bagaimana Anda menggunakan aturan rantai untuk membedakan f (x) = sin (tan (5 + 1 / x) -7x)?
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