Hvordan adskiller du den følgende parametriske ligning: x (t) = t / (t-4), y (t) = 1 / (1-t ^ 2)?

Hvordan adskiller du den følgende parametriske ligning: x (t) = t / (t-4), y (t) = 1 / (1-t ^ 2)?
Anonim

Svar:

# Dy / dx = - (t (t-4) ^ 2) / (2 (1-t ^ 2) ^ 2) = - t / 2 ((t-4) / (1-t ^ 2)) ^ 2 #

Forklaring:

# Dy / dx = (y '(t)) / (x' (t)) #

#Y (t) = 1 / (1-t ^ 2) #

#Y '(t) = ((1-t ^ 2) d / dt 1 -1d / dt 1-t ^ 2) / (1-t ^ 2) ^ 2 #

#COLOR (hvid) (y '(t)) = (- (- 2t)) / (1-t ^ 2) ^ 2 #

#COLOR (hvid) (y '(t)) = (2t) / (1-t ^ 2) ^ 2 #

#x (t) = t / (t-4) #

# x '(t) = ((t-4) d / dt t -t d / dt t-4) / (t-4)

#COLOR (hvid) (x '(t)) = (t-4-t) / (t-4) ^ 2 #

#COLOR (hvid) (x '(t)) = - 4 / (t-4) ^ 2 #

# Dy / dx = (2t) / (1-t ^ 2) ^ 2 -: - 4 / (t-4) ^ 2 = (2t) / (1-t ^ 2) ^ 2xx- (t-4) ^ 2/4 = (- 2t (t-4) ^ 2) / (4 (1-t ^ 2) ^ 2) = - (t (t-4) ^ 2) / (2 (1-t ^ 2) ^ 2) = - t / 2 ((t-4) / (1-t ^ 2)) ^ 2 #