Y=x/x+Y, then dy/dx=

Question

Calculus AB

Answer 1

There should be parentheses around denominator, (x+y)...otherwise this equation is equivalent to 0 = 1.

Multiply to get y(x+y) = x, i.e. y² + xy = x.

 

Now use implicit differentiation:  2yy' + y + xy' = 1

and you can proceed from here, I know, to solve for y' (another name for dy/dx).