docs: clarify multithreading limitations (#923)

Author: gdalle

DifferentiationInterface/docs/src/faq/limitations.md

@@ -1,5 +1,37 @@
 # Limitations
 
+## Multithreading
+
+The preparation result `prep` is not thread-safe, since it usually contains values that are mutated by differentiation calls.
+Sharing it between threads may lead to unexpected behavior or errors.
+If you need to run differentiation concurrently, construct a separate `prep` object for each thread, for instance with the help of [OhMyThreads.jl](https://github.com/JuliaFolds2/OhMyThreads.jl).
+
+Note that functions which use multithreading internally are completely fine:
+
+```julia
+function f!(y, x)
+    @threads for i in eachindex(y, x)
+        y[i] = x[i]
+    end
+    return nothing
+end
+
+# this is correct
+prep = prepare_jacobian(f!, y, backend, x)
+J = jacobian(f!, y, prep, backend, x)
+```
+
+The pattern we are warning about concerns multithreading outside of the function:
+
+```julia
+# this is incorrect
+prep = prepare_jacobian(f!, y, backend, x)
+@threads for k in 1:n
+    # same prep object, different threads writing to it
+    J = jacobian(f!, ys[k], prep, backend, xs[k])
+end
+```
+
 ## Multiple active arguments
 
 At the moment, most backends cannot work with multiple active (differentiated) arguments.