Question

If `y=xsin(x+y)`, then what is `dy/dx`?

Answer 1

`y' =(sin(x+y) + x cos(x+y) )/( 1 - x cos(x+y) )`

Explanation:

`y=xsin(x+y)`

By the Product and Chain Rules:

`y' =sin(x+y) + x cos(x+y) (1 + y')`

`y' ( 1 - x cos(x+y) ) =sin(x+y) + x cos(x+y)`

`y' =(sin(x+y) + x cos(x+y) )/( 1 - x cos(x+y) )`