Kako najdete derivat sqrt (1-x ^ 2)?

Odgovor:

# (dy) / (dx) = - x (1-x ^ 2) ^ (- 1/2) #

Pojasnilo:

Uporabi pravilo verige:

# (dy) / (dx) = (dy) / (du) #x# (du) / (dx) #

Let # u = 1-x ^ 2 #, potem # (du) / (dx) = - 2x # in # dy / (du) = 1/2 (1-x ^ 2) ^ (- 1/2) #

Priključite ga v pravilo verige,

# (dy) / (dx) = - 2x x # 1/2 (1-x ^ 2) ^ (- 1/2) = - x (1-x ^ 2) ^ (- 1/2) #

Kaj je (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?

2/7 vzamemo, A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5) -sqrt3) / (2sqrt3-sqrt5) = (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5) ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15-5 + 2 * 3-sqrt15)) / ((2sqrt3)) ^ 2- (sqrt5) ^ 2) = (prekliči (2sqrt15) -5 + 2 * 3zaključi (-sqrt15) - prekliči (2sqrt15) -5 + 2 * 3 + prekliči (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Upoštevajte, da če je v imenovalcu (sqrt3 + sqrt (3 + sqrt5)) in (sqrt3 + sqrt (3-sqrt5)), bo odgovor spremenjen.

Kako najdete derivat sqrt (x ln (x ^ 4))?

(ln (x ^ 4) +4) / (2sqrt (xln (x ^ 4))) Ponovno ga napišite kot: [(xln (x ^ 4)) ^ (1/2)] 'Sedaj moramo izpeljati iz zunaj navznoter z uporabo pravila verige. 1/2 [xln (x ^ 4)] ^ (- 1/2) * [xln (x ^ 4)] 'Tu dobimo derivat produkta 1/2 (xln (x ^ 4)) ^ (- 1/2) * [(x ') ln (x ^ 4) + x (ln (x ^ 4))'] 1/2 (xln (x ^ 4)) ^ (- 1/2) * [1 * ln (x ^ 4) + x (1 / x ^ 4 * 4x ^ 3)] Samo z uporabo osnovne algebre, da dobimo vmesno različico: 1/2 (xln (x ^ 4)) ^ (- 1/2) * [ ln (x ^ 4) +4] In dobimo rešitev: (ln (x ^ 4) +4) / (2sqrt (xln (x ^ 4))) Mimogrede lahko celo napišete začetni problem, da ga naredimo bolj preprosto: s

Kako poenostavite (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / ( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Ogromno oblikovanje matematike ...> barva (modra) (((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))) = barva (rdeča) (((1 / sqrt (a- 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = barva ( modro) ((((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a -1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = barva (rdeča) ((1 / sqr