2014 04 19 

Mike Polioudakis 

Using Liebnitz’s derivative notation 

Newton invented the “prime” (‘ and ‘’ and ‘’’) notation for derivatives.  Liebnitz invented the notation most used today:  d/dx  d2/x2  d3/x3  and etc.  The world adopted Liebnitz’ notation, mostly because his notation is intuitive and it helps in solving some problems.  I need help understanding how it helps.  Mathematicians sometimes treat “d/dx” as a literal fraction, split up the “d” from the “dx”, and then manipulate the two quantities.  I can usually understand when a mathematician does this.  I can’t see in advance when I could do it to make my own work easier.  I can’t always understand how a mathematician saw it in before he-she set to work on a problem.  I need practice working problems where this technique is used.  Hopefully the problems start out simple and get more complex.  Hopefully there are a lot of simple problems.  If you have any suggestions, I would appreciate it.  

I think this knowledge, and the resultant skill, would be useful to other people.  If I get enough examples, and make up a lot of examples of my own, I will either put it all on this website, or publish it in some other venue.  If you help me, I gladly will acknowledge your help in appropriate detail.