Kako najdete derivat f (x) = sqrt (^ 2 + x ^ 2)?

Odgovor:

#f '(x) = x / (sqrt (a ^ 2 + x ^ 2)) #

Pojasnilo:

Pravilo verige je takšno:

Če #f (x) = (g (x)) ^ n #, potem #f '(x) = n (g (x)) ^ (n-1) * d / dxg (x) #

Uporaba tega pravila:

#f (x) = sqrt (^ 2 + x ^ 2) = (a ^ 2 + x ^ 2) ^ (1/2) #

#f '(x) = 1/2 (a ^ 2 + x ^ 2) ^ (1 / 2-1) * d / dx (a ^ 2 + x ^ 2) #

#f '(x) = 1/2 (a ^ 2 + x ^ 2) ^ (- 1/2) * 2x #

#f '(x) = 1 / (2 (a ^ 2 + x ^ 2) ^ (1/2)) * 2x #

#f '(x) = x / ((^ 2 + x ^ 2) ^ (1/2)) #

#f '(x) = x / (sqrt (a ^ 2 + x ^ 2)) #