Question

if x+y=sin (x+y) prove that dy/dx =1

Answer 1

x+y = sin (x+y)
d/dx (x+y) = d/dx (sin (x+y))
by chain rules on d/dx (sin(x+y))
d/dx x + d/dx y = d/dx (sin (x+y) d/dx (x+y)
1 + dy/dx = cos (x+y) (1+dy/dx )
1+dy/dx = cos(x+y) + cos (x+y) dy/dx
1 - cos (x+y) = cos (x+y) dy/dx - dy/dx
1-cos (x+y) = -dy/dx [ 1 - cos (x+y)]
dy/dx= -1