Derivative work in photography is something that is similar to someone else's, and is recognized to be such. Calling a work "derivative" is usually derogatory.
If I go to Yosemite to photograph, I don't want someone saying that my pictures look like I found Ansel Adams' tripod holes and I put my camera over them. I love Adams' work, but I don't want mine to look like his.
I want my pictures to be recognizably mine. The last thing I want to hear is that they look derivative.
It's OK to study the masters and to even try to copy them as a learner. Most great artists have done that as they were perfecting their craft and style. I find myself doing the same thing when I "reverse engineer" a great photo I see in a gallery or on the web, then make a mental note to try that same perspective, angle, lighting, or process.
But to go where my own growth leads me is to go down my own path where no one else can go. No one else can go there because no one else is me.
The best way to avoid producing derivative work is to be myself as much as possible.
Chase Jarvis addressed this issue recently. He wrote in his blog that "you should strive to make a photograph that no one else in the world can make. And the primary mode of being able to do this is to infuse your personal vision to the image. Period."
From an entirely different vantage point, writing about marketing and differentiation in the world of business in his book ZAG: The #1 Strategy of High-Performance Brands, author Marty Neumeier calls this kind of uniqueness a zag (as in zag when others zig). "'Onliness' is the true test of a zag. If you can't say you're the 'only,' go back and start over."
As photographers, we start with the world that we photograph. This is available to anyone with a camera. It's our raw material, like a slab of clay to a potter. What we personally bring to this world are our developed skills and techniques, vision, insight, taste, preferences, timing, style, etc. The aggregate constitutes our "onliness." Most importantly, our "onliness" includes how we relate to our world, interact with it, and walk through it. It includes how heavy our step is, where we place our gaze, and how we allow our eyes to see.
How can I be myself? For me, it starts by relaxing and finding a place of comfort. It starts by detaching a bit, noticing without judgment, and welcoming all that enters my space, the only space that is mine alone.
It's a process of relaxation, gently noticing, and connecting when the fit is right. When I genuinely inhabit this place, the only things I can photograph there are derivative from me alone.