A point moves on the hyperbola $\displaystyle x^2-4y^2=36$ in such a way that the x-coordinate increases at a constant rate of 20 units per second. How fast is the y-coordinate changing at the point (10,4)?

$\displaystyle 4y^2=x^2-36$

$\displaystyle 8y*\frac{dy}{dt}=2x*\frac{dx}{dt}-0$

$\displaystyle \frac{dy}{dt}=\frac{2x*\frac{dx}{dt}}{8y}$

$\displaystyle \frac{dy}{dt}=\frac{(2)(10)(20)}{(8)(4)}$

$\displaystyle \frac{dy}{dt}=\frac{400}{32}=\frac{25}{2}$units per second is what I come up with.

The book, however, provides an answer of 50 units/sec

Did I mess this one up?