Point A moves along the x-axis at the constant rate of a ft/s while point B moves along the y-axis at the constant rate of b ft/s. Find how fast the distance between them is changing when A is at the point $(x,0)$ and B is at the point $(0,y)$.
I found this question in a textbook on Calculus and Analytic Geometry. I approached it very mechanically: the known constants are $dx\over dt$$= a$ and $dy \over dt$$= b$. The length between the two points can be found from $(x^2 + y^2)^{1/2}$. Call this length function $l$. Know, I found the derivative of this length function to be $ax + by \over l$ which doesn't seem to be constant. What am I doing wrong? Thank you in advance.