title: finding the derivative of a polynomial
body: <p>I wondering symbolically how you would parse a polynomial into a function and return the derivative. What data structure would I use or method to parse the polynomial? Preferably without using any libraries, as this question could pop up in a technical interview. </p>
  
  <pre><code>polynomial-&gt; of nth degree
  
  def derivative(polynomial):
      return derivative
  
  Example:
  
  f(x)  = 2x^2+3x+1
  f'(x) = 4x+3
  </code></pre>
  
  <p>I don't want a solution, this is not homework but a hint of where I would start.</p>