Question

dy/dx=sin (x+y) +cos (x+y)

Answer 1

hey mate here is your answer
y=sin(x+y)+cos(x+y)
diff w.r.t x
$\frac{dy}{dx} = cos(x + y) (1 + \frac{dy}{dx} ) - sin(x + y)(1 + \frac{dy}{dx} \\ = cos(x + y) + cos(x + y) \times \frac{dy}{dx} - \sin(x + y) - \sin(x + y) \times \frac{dy}{dx} \\ \frac{dy}{dx} - \cos(x + y) \times \frac{dy}{dx} + \sin(x + y) \frac{dy}{dx} = cos(x + y) - sin(x + y) \\ \frac{dy}{dx} = \frac{ \cos(x + y) - \sin(x + y) }{sin(x + y) - \cos(x + y) }$