Interestingly enough the derivative functions are available to compute shaders as of SM 6.6. [0] Oddly SPIR-V only makes the associated opcodes [1] available to the fragment execution model for some reason. I'm not sure how something like DXVK handles that.
I'm not clear if the associated DXIL or SPIR-V opcodes are actually implemented in hardware. I couldn't immediately find anything relevant in the particular ISA I checked and I'm nowhere near motivated enough to go digging through the Mesa source code to see how the magic happens. Relevant because since you mentioned it I'm curious how much of a perf hit rolling your own is.
[0] https://microsoft.github.io/DirectX-Specs/d3d/HLSL_SM_6_6_De...
[1] https://registry.khronos.org/SPIR-V/specs/unified1/SPIRV.htm...