Implicit differentiation, what am I doing wrong?

Use implicit differentiation to find dy/dx for cos(x+y) + sin(x+y) = 0.5

Differentiating this I got -sin(x+y)(1+dy/dx) + cos(x+y)(1+dy/dx) = 0

Try factorising at this point.

Edit: You don't actually need implicit differentiation for this question, and could use the sum/product trig. rules, if you've covered them.

I factorised dy/dx and made it the subject as thats what you are trying to find?

Use implicit differentiation to find dy/dx for cos(x+y) + sin(x+y) = 0.5

Differentiating this I got -sin(x+y)(1+dy/dx) + cos(x+y)(1+dy/dx) = 0

I rearranged this to get dy/dx = sin(x+y) - cos(x+y) / cos(x+y) - sin (x+y)

Then using the given equation I rearranged and got

-cos (x+y) = -0.5 +sin(x+y)
and -sin(x+y) = -0.5 + (cosx+y)
and tried subbing in my dy/dx but it gives some other expression, the answer should just be -1

where do I go from here?

Thanks

Dalek isn't trolling in case people are suspicious. He did fail to say that you need to make the implicit equation equal to zero before using this technique.

I can't agree that this is any easier than ghostwalker's method though.

Is it just (1+dy/dx) (cos(x+y) - sin (x+y)) = 0? then you can get dy/dx = -1? but I dont see why cos (x+y) - sin (x+y) = 0?