GeoGebra

It's nice as long as you don't need to use the log scale on the x or y axis. I could not find a way to do it. Very disappointed! :(

Lies about being open source. https://www.mail-archive.com/license-discuss@lists.opensource.org/msg01915.html

It is the best of best for science & maths both for student & teacher

I use Geogebra for creating educational images and dynamically exploring geometry. However, the snapping system is limited and does not inspire confidence. The undo / redo system includes zooming and panning, and has always been filled with bugs. These two things become more apparent when working on complex constructions with many objects. If you are interested in a program for geometric construction and exploration, then I recommend trying LibreCad.

This is a highly-respected package with many test files available across the web and an excellent help system. It can differentiate, integrate, perform many geometric functions, use multiple colours, be interactive, and you can even send files to your students to use them at home since they do not need to pay to get a licence for the software.