Is that from Arnold? (it's not an option on a vanilla bump2d) This was the first hit on google for me.
"Enables the use of derivative normal maps. If you disable 'Use Derivatives' when using tangent-space normal mapping, the bump shader uses the tangent and bitangent data stored on the mesh. Otherwise (by default), the bump shader will use the UV surface derivatives from the Arnold shading globals."
So a potential use-case for this would be when you've baked something specifically for a low poly mesh VS tiling a normal map over complex forms maybe? When you've baked something specifically for a LP object, you'll want to use their tangent/bi-normals since your normal map is baked to consider them. If you're tiling a texture you might want to disregard the objects normals? and it wouldn't make a difference on a flat plane? Cheers.
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"Enables the use of derivative normal maps. If you disable 'Use Derivatives' when using tangent-space normal mapping, the bump shader uses the tangent and bitangent data stored on the mesh. Otherwise (by default), the bump shader will use the UV surface derivatives from the Arnold shading globals."