Hi could someone please explain to me how i would use the chain rule

Question

dy/dx = dy/du(du/dx) to solve for
y= sin(x+y) - im looking for dy/dx
i don't understand the steps
thanks

Answer 1

let u = x + y
du/dx = 1 + dy/dx

then y = sin u
and dy/dx = cosu du/dx
= cosu (1 + dy/dx)
= cosu + dy/dxcosu
dy/dx - dy/dxcoxu = cosu
dy/dx = cosu/(1 - cosu)
= cos(x+y)/( 1 - cos(x+y)

personally I would bypass all that subbing and my second line would be

dy/dx = cos(x+y)(1 + dy/dx)
etc.

Answer 2

alright, but i don't know how i would now isolate for dy/dx?