Prepositions – The Correct Preposition After “Consumption”

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.

In such cases, as a learner, I suggest that you check the Oxford dictionary. It always provides many nice examples through which you can discover the idiomatic sentences and collocations. By the way, the idiomatic preposition is to.

You can say

I plan to travel to China

In terms of your second question. You can use those prepositions in different context. For instance, you can say:

• It's really interesting to travel in groups.
• It's really easy to travel in the USA.

(Using "in" when talking about the place itself like USA, Canada,... and when describing the way of traveling)

Or

• I traveled for a month.
• I traveled for a business goal.

(Using "for" when talking about reason or duration)

By the way, our native friend on ELL can provide you with more accurate and idiomatic examples. I thought It's a good idea to mention some myself.