Slope of tangent at ordinate ln 3 is

Question

A curve passing through origin is such that slope of tangent at any point is reciprocal of sum of coordinate of point of tangents.

Slope of tangent at ordinate ln 3 is

(A) 1

(B) 1/3

(C) 1/2

(D) - 2

Answer 1

Answer is (C) 1/2

dy/dx = 1/(x + y)

Let x + y = v. Then

1 + dy/dx = dv/dx

⇒ dv/dx = 1/v + 1 = (1 + v)/v