Hvordan finder du derivatet af f (x) = sqrt (a ^ 2 + x ^ 2)?

Svar:

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

Forklaring:

Kædelegemet går som følger:

Hvis #f (x) = (g (x)) ^ n #, derefter #F '(x) = n (g (x)) ^ (n-1) * d / DXG (x) #

Anvendelse af denne regel:

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

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

Hvordan finder du derivatet af sqrt (x ln (x ^ 4))?

(ln (x ^ 4) +4) / (2sqrt (xln (x ^ 4))) Lad os omskrive det som: [(xln (x ^ 4)) ^ (1/2)] 'Nu skal vi aflede fra ydersiden til indersiden ved hjælp af kædelegemet. 1/2 [xln (x ^ 4)] ^ (- 1/2) * [xln (x ^ 4)] 'Her har vi et derivat af et produkt 1/2 (xln (x ^ 4)) ^ 1/2 (xl)) x (ln (x ^ 4))]] 1/2 (xln (x ^ 4)) ^ (- 1/2) * [1 * ln (x ^ 4) + x (1 / x ^ 4 * 4x ^ 3)] Brug blot basisalgebra for at få en semplificeret version: 1/2 (xln (x ^ 4)) ^ (- 1/2) * [ ln (x ^ 4) +4] Og vi får løsningen: (ln (x ^ 4) +4) / (2sqrt (xln (x ^ 4)) Forresten kan du endda omskrive det initale problem for at gøre

Hvordan finder du derivatet af sqrt (2x-3)?

F (x) = 1 / (2x3)) f (x) = sqrt (2x-3) f '(x) = 1 / (2sqrt (2x-3)) * 2f' = 1 / (cancel2sqrt (2x-3)) * cancel2 f '(x) = 1 / (sqrt (2x-3))

Hvordan forenkler du (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Kæmpe matematisk formatering ...> farve (blå) ((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = farve (rød) 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1))) / +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = farve blå) ((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt -1)))) (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = farve / (Sqrt (a-1) -sqrt (a + 1)) / (sqrt (a +