Here's a homework problem from the Coursera course [Calculus: Single Variable by Robert Ghrist](https://www.coursera.org/course/calcsing)

> 
> Find the derivative $\frac{dy}{dx}$ from the equation $x \tan y - y^2 \ln x=4$
> 
> 
> 

I wanted to check my work using Mathematica so I tried this:

```
Dt[x Tan[y] - y^2 Log[x] == 4];
% /. {Dt[y] -> dy, Dt[x] -> dx};
Reduce[{%, dy/dx == z}, z]

```

On my system (Mathematica 9, Windows 7), this computation seems to hang.

Does anyone have a suggestion on how to solve this?

**Edit:**

I'm also interested in why `Reduce` doesn't handle the problem well when used as above whereas `Solve` handles it just fine (see answers).