Responda:
# dy / dx = - (2sin (x-y) + 2xcos (x-y)) / (1-2xcos (x-y)) #
Explicação:
Podemos reorganizar e simplificar para obter:
# -2xsin (x-y) = y #
# d / dx y = d / dx -2xsin (x-y) #
# d / dx y = d / dx -2x sen (x-y) -2xd / dx sen (x-y) #
# d / dx y = - 2sin (x-y) -2xd / dx sen (x-y) #
# d / dx y = - 2sin (x-y) -2xcos (x-y) d / dx x-y #
# d / dx y = - 2sin (x-y) -2xcos (x-y) (d / dx x -d / dx y) #
# d / dx y = - 2sin (x-y) -2xcos (x-y) (d / dx x -d / dx y) #
Usando a regra chqain, conseguimos # d / dx = dy / dx * d / d #
# dy / dxd / dy y = - 2sin (x-y) -2xcos (x-y) (1-dy / dxd / dy y) #
# dy / dx = -2sin (x-y) -2xcos (x-y) (1-dy / dx) #
# dy / dx = -2sin (x-y) -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)) #
