title: How to find a function's rth derivative when r is symbolic in Mathematica?
body: <p>I have a function <code>f(t)=2/(2-t)</code>. It is not so hard to get the rth derivative at t=0 (i.e.  <code>2^(-r)*r!</code>) without using Mathematica. In the case of Mathematica calculation, I can get the r-th derivative when r=4 like this: <code>D[2/(2-t), {t, 4}]</code>. But how can I get the rth derivative at t=0 in Mathematica when r is ANY integer?  I tried to use this expression, but it didn't work as expected:</p>
  
  <pre><code>Simplify[D[2/(2 - t), {t, r}], Assumptions -&gt; Element[r, Integers]]  /. {t-&gt;0}
  </code></pre>
  
  <p>Is it possible to do the above math symbolically in Mathematica just as we humans do?</p>