Related Rates: Derivatives and Distance in the XY-Plane

[kuahji]

Let x & y be differentiable functions of t and let s = sqrt(x^2+y^2) be the distance between the points (x,0) and (0,y) in the xy-plane.

How is ds/dt related to dx/dt if y is constant?

So I attempted to implicitly take the derivatives of the changing rates.

ds/dt= 1/(2sqrt(x^2+y^2)) times 2x dx/dt + 2y

Which simplifies to

ds/dt= x/(sqrt(x^2+y^2)) dx/dt + y/(sqrt(x^2+y^2))

I'm guessing there is something I'm not understanding because he book shows an answer of ds/dt= x/(sqrt(x^2+y^2)) dx/dt

So what y does the y disappear? Or what am I doing incorrectly?

 

[Dick]

Ummm. "if y is constant" says the problem. On such a path, dy/dt=0.