Hvad er derivatet af y = 5 ^ sqrt (s)?

Svar:

# Dy / (ds) = (log (5) 5 ^ sqrt (r)) / (2sqrt (e)) #

Forklaring:

Brug kæden brug:

#F (x) = g (h (x)) => f '(x) = h' (x) g '(h (x)) #

Med:

#g (u) = 5 ^ u => g «(u) = log (5) 5 ^ u #

#t (x) = sqrt (x) => 1 / (2sqrt (x)) #

At sætte dette sammen har vi:

# Dy / (ds) = (log (5) 5 ^ sqrt (r)) / (2sqrt (e)) #

Hvad er (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (3-) sqrt (5))?

2/7 Vi tager A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - -sqrt3) / (2sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (sqrt5-sqrt5) ) (2sqrt3 + sqrt5)) / ((2sqrt3 + sqrt5) (2sqrt3-sqrt5) = ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) / ((2sqrt3) ^ 2- (sqrt5) ^ 2) = (annullere (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - annullere (2sqrt15) -5 + 2 * 3 + annullere (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Bemærk, at hvis i betegnelserne er (sqrt3 + sqrt (3 + sqrt5)) og (sqrt3 + sq

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 +

Hvordan bruger du grænse definitionen af derivatet for at finde derivatet af y = -4x-2?

-4 Definitionen af derivat er angivet som følger: lim (h-> 0) (f (x + h) -f (x)) / h Lad os anvende ovenstående formel på den givne funktion: lim (h-> 0) (f (x + h) -f (x)) / h = lim (h-> 0) (- 4 (x + h) -2 - (- 4x-2)) / h = lim (h-> 0 ) (- 4x-4h-2 + 4x + 2) / h = lim (h-> 0) ((- 4h) / h) Forenkling ved h = lim (h-> 0) (- 4) = -4