Question

Find dy/dx if y=sin (x+y)

Answer 1

\[\cos(x+y).(\frac{ d }{ dx } y+1)\rightarrow \frac{ d }{ dx } y =\frac{ 1 - \cos (x+y) }{ \cos (x+y) }\]

Answer 2

I would rewrite sin( x+y) as sinxcosy+cosxsiny and differentiate that using implicit differentiation when needed.