Verified answer

Derivative of the left side:

d( ln(x+y) )/dx

1/(x+y) *d(x+y)/x

1(x+y) * (1 + dy/dx)

Derivative of the right side:

d( arctan(y) )/dx

1/(y^2+1) * d(y)/dx

Set these two equal and perform algebraic manipulations to solve for dy/dx:

1(x+y) * (1 + dy/dx) = 1/(y^2+1) * d(y)/dx

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dy/dx = (y^2 + 1) / (x + y - y^2 - 1)