
rate of change
A point moves along the curve y = x^2 + 1 so that the xcoordinate is increasing at the constant rate of 3/2 units per second. What is the rate, in units per second, at which the distance from the origin is changing when the point has coordinate (1,2)?
I thought that $\displaystyle \frac {2}{3} x = t$ and that would make $\displaystyle \frac {2}{3} \sqrt{(y1)} = t$ and then I would only have to find the rate of change, but I think thats wrong.

$\displaystyle y = x^{2} + 1$
$\displaystyle dy = 2x(dx)$
Given x = 1 and dx = 3/2, calculating dy is simple.