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I have this sentence:
Moreover, spelling’s error patterns and statistical trends can be derived (from /by/through/by means of) the software.
It means that the software outputs some statistical results in which some patterns can be discovered.
What is the best preposition for my meaning. Or even an equivalent sentence. "From" is the collocation word but I am afraid it is not applicable here.
It depends on what you're trying to say:
X is derived from Y.
In this case Y is what forms the basis for X, so X is based on Y.
X is derived through Y.
Here Y is what performs the action, but X is derived from something else. Y just makes the action of deriving happen.
X is derived by Y.
In this case, Y would most likely be an action that starts the action of deriving. For example:
You can derive X from Y by clicking Z.
In your sentence, through would fit best as I suppose it is the software that does the deriving for the user.
X is derived from Y - X is something we obtained from Y.
X is derived by Y - Y is a method or tool used to obtain X. What X was derived from is not said.
X is derived through Y - this means the same as X derived by Y.
