Answer
$\frac{1}{u}$
Work Step by Step
Step 1. Letting $cot^{-1}u=t$, we have $cot(t)=u$ and $-\frac{\pi}{2}\le t \le \frac{\pi}{2}$
Step 2. Form a right triangle with sides $y=1,x=|u|,r=\sqrt {u^2+1}$.
Step 3. As $tan(t)$ and $cot(t)$ have the same sign in the above interval, we have $tan(cot^{-1}u)=tan(t)=\frac{1}{u}$