Kako ločite f (x) = (x ^ 3-2x + 3) ^ (3/2) z uporabo verižnega pravila?

Odgovor:

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

Pojasnilo:

Pravilo verige:

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

Pravilo moči:

# d / dx x ^ n = n * x ^ (n-1) #

Uporaba teh pravil:

1 Notranja funkcija, #g (x) # je # x ^ 3-2x + 3 #, zunanja funkcija, #f (x) # je #g (x) ^ (3/2) #

2. Vzemite derivat zunanje funkcije s pravilom moči

# d / dx (g (x)) ^ (3/2) = 3/2 * g (x) ^ (3/2 - 2/2) = 3/2 * g (x) ^ (1/2) = 3/2 * sqrt (g (x)) #

#f '(g (x)) = 3/2 * sqrt (x ^ 3 - 2x + 3) #

3. Vzemite izpeljanko notranje funkcije

# d / dx g (x) = 3x ^ 2 -2

#g '(x) = 3x ^ 2 -2

4 Pomnožite #f '(g (x)) # z #g '(x) #

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

rešitev: # 3/2 * (sqrt (x ^ 3 - 2x + 3)) * (3x ^ 2 - 2) #

Kako ločite f (x) = sqrt (ln (x ^ 2 + 3) z uporabo verižnega pravila.?

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))) Dobili smo: 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)))

Kako ločite f (x) = ln (sinx) ^ 2 / (x ^ 2ln (cos ^ 2x ^ 2)) z uporabo verižnega pravila?

Glejte spodnji odgovor:

Kako ločite f (x) = tan (e ^ ((lnx-2) ^ 2)) z uporabo verižnega pravila.

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