Resposta:
# dy / dx = - (2sin (x-y) + 2xcos (x-y)) / (1-2xcos (x-y)) #
Explicació:
Podem reorganitzar i simplificar per obtenir:
# -2xsin (x-y) = y #
# d / dx y = d / dx -2xsin (x-y) #
# d / dx i = d / dx -2x sin (x-y) -2xd / dx sin (x-y) #
# d / dx y = - 2s (x-i) -2xd / dx sin (x-y) #
# d / dx y = - 2in (x-i) -2xcos (x-i) d / dx x-i #
# d / dx y = - 2in (x-i) -2xcos (x-i) (d / dx x -d / dx i) #
# d / dx y = - 2in (x-i) -2xcos (x-i) (d / dx x -d / dx i) #
Utilitzant la regla chqain ho aconseguim # d / dx = dy / dx * d / dy #
# dy / dxd / dy i = - 2sin (x-i) -2xcos (x-i) (1-dy / dxd / dy i) #
# dy / dx = -2sin (x-y) -2xcos (x-y) (1-dy / dx) #
# dy / dx = -2sin (x-i) -2xcos (x-y) + 2xcos (x-y) dy / dx #
# dy / dx-2xcos (x-y) dy / dx = -2sin (x-y) -2xcos (x-y) #
# dy / dx 1-2xcos (x-y) = - 2sin (x-y) -2xcos (x-y) #
# dy / dx = - (2sin (x-y) + 2xcos (x-y)) / (1-2xcos (x-y)) #
