Question

Find dy/dx if x sin y + y sin x = 0.

Answer 1

x sin y + y sin x = 0
Differentiate w.r.t. x both side

`[xcosy dy/dx+siny]+[ycosx+sinxdy/dx]=0`

`therefore siny+ycosx=dy/dx(-sinx-xcosy)`

`therefore dy/dx=-((siny+ycosx)/(sinx+xcosy))`