Question

if y=sin(x+y) find dy/dx​

Answer 1

Answer:

cos(x+y) / [1-cos(x+y)]

Step-by-step explanation:

y = sinxcosy + cosxsiny

dy/dx = sinx.d/dx(cosy)+ cosy.d/dx(sinx) + cosx.d/dx(siny)+ siny.d/dx(cosx)

         = sinx (-siny)dy/dx + cosy(cosx) + cosx.(cosy)dy/dx + siny.(-sinx)

dy/dx + sinxsinydy/dx- coxcosydy/dx = cosxcosy - sinxsiny

//remember cos(x+y) = cosxcosy - sinxsiny

dy/dx[ 1 - cosxcosy+sinxsiny]    =  cosxcosy - sinxsiny

dy/dx [ 1 - cos(x+y)] = cos(x+y)

dy/dx = cos(x+y) / [1-cos(x+y)]