I don't see any errors in your derivation. I would say the book is wrong.
A point moves on the hyperbola 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)?
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?