Partial Derivatives & the Gradient · Challenge problem

Let $f(x,y) = x^2 y$ and $g(x,y) = x + y^2$. A particle starts at $(1,2)$ and moves along the level curve of $f$ through that point, heading in the direction in which $x$ increases. Find the rate of change of $g$ per unit distance travelled at the moment it leaves $(1,2)$.