implicit differentiation

well i know all of that but if you move (cos x- sin y dy/dx) to the other side, which sign will be changed like will it become -(cos x-sin y dy/dx)?

I've attached my workings.

I think what's happened is you've confused your negative and positive signs. I would rewrite anything that looks like cosx-siny to -cosxsiny as it makes it clearer when doing the rest of your workings

You can do this because you know that multiplying a positive by a negative will give a negative answer.

yeah that's exactly what my problem was but thanks for your working made it clear but don't you think cos y cos x should be positive before rearranging process starts?

cosycosx comes from differentiating the product run cosysinx so yeah you're right.

I got equally muddled with my signs trying to write on small bits of paper but glad it makes sense

AQA page 86 question 10 part b

what year ?