Lets start off with what Derivative works are.

Derivative

something derived.

Derived

to take, receive, or obtain especially from a specified source.

So how do you keep from making an error and how do you know.

• If you open a graphic in any paint program and change even one pixel of color or save it in a different format (ie jpg to gif); then you have made a derivative.

• If you take one graphic and incorporate pieces of it into your own creation than you have made a derivative.

• If you change the color, perspective or size (even using html values to change the size) then you have created a derivative.

• If you take a background graphic and use it for a card, wallpaper, or any other use not originally intended then you have made a derivative.

• When you compress a graphic it takes pixels of color out. This makes them load faster but reduces the quality and is also a derivative. Another thing to think about is that this is an injustice to the artist. They try to make their best and compressing their work makes it into something they would be ashamed to be associated with.
  Now derivative works go much farther than our graphics example. It extends to all intellectual property; writing, music, photography, movies, sculpting etc.

  One area that most people don't think about is Fan fiction. This is where someone writes a story using Characters from a copyright work. Now alot of production companies may turn a blind eye to this practice and even scan them for ideas, BUT it is still against copyright law and could wind you up in court.

  If I find a poem that I thought was perfect except for a couple of words. I could not make those 'corrections'. This would be a derivative work and infringing on the poets copyright.

  The U.S. copyright office maintains an FAQ. One of the questions states

  "How much do I have to change in order to claim copyright in someone else's work?
  Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create a new version of that work. Accordingly, you cannot claim copyright to another's work, no matter how much you change it, unless you have the owner's consent. See Circular 14."

  It doesn't matter if you think it looks better or sounds better, the copyright holder is the only one that can legally make changes to their orignial work.

  A good rule of thumb when using anyone elses work

  Don't alter it
  Don't add to it
  don't use pieces of it