The first usage seems to indicate some sort of extractive process, such as mining: coal is obtained from the earth, for example. The second indicates more of a process (even if it might be the same process, but now the process is specified): coal is obtained by mining.

In general, the word “from” will point to a geographical or literal source of some kind, and “by” shows more of a “how” – at least to this reader.

I agree with @CWOTUS but @tianxiaweigong could you give us the whole sentence so that we can help you find the correct one?

I would say the first should be followed by a noun and the second by a verb.

The first phrase answers the question “Where?”
“Where was X obtained from?”
“It was obtained from here.”

The second phrase answers the question “Who?”
“Who was it obtained by?”
“It was obtained by X.”

In the first phrase, X is the objective, and in the second, X is the subjective.
“From” indicates place of origin. “Where from?”
“By” (here) indicates the doer. “By whom?”

That is at last one way to put it. If you want anything specific, you’d have to give concrete sentences, as @Stinley said.

“From”—source. “By”—- method

Both are very indirect, inactive ways of saying something. What is the sentence?

I imagine that the context is mathematical.

As in ” the square root of 43 is obtained by ....”

How to think about them? The difference is in the little word at the end. In these two instances, the meaning of “obtained” doesn’t change, but the preposition changes the whole expression. You could even use both ideas together: “X is obtained from Y by Z.”

@stanleybmanly, yes. Method (process) or agent.

Both call for nouns (even if a verbal noun) because both “from” and “by” are prepositions requiring a noun as object.

They’re not indirect. They’re just passive. In many contexts, especially technical, this is just fine.

Thanks all of you！