Even if the source is 'right,' it might not pick up the context necessary to answer the question appropriately. I would consider the fact that different prompts resulted in different answers to what is effectively the same question might support that idea.

Maybe ChatGPT could actually give someone the answer of how to make meth correctly if given the right prompt, but in order to even know how to phrase it you'd need to know quite a bit of chemistry- and at that point, you could just as easily figure it out yourself with a pen and paper. That has the added upside of the DEA not kicking in your door for "just asking questions" too.

As far as calculus goes, I can imagine some of the inputs might be confusing to an AI that is not specifically trained for them since the minutiae of formatting is essential. There might be something inherent to calculus that the AI has difficulty understanding, or it might just be user error too. It's hard to say.

Edit: the other guy who responded's explanation is more correct, listen to them. My background in CS is woefully lacking, but their answer seems right based on my limited understanding of how this AI works.

It's an algorithm trained to mimic human output from a prompt. It's only as good as what it was trained on, and people in general suck at hard science and advanced math.

Take, for example, how people 'tricked' ChatGPT into telling them how to make meth. It actually would give them different answers based on how they asked the question, and just in the off-chance that isn't obvious, is not how chemistry works. Also I never saw it give an answer that was actually 'right' in terms of organic chemistry, either for pure pharmaceutical grade methamphetamine (aka Desoxyn) or street meth. It sure seemed right if you didn't understand the actual chemistry. It seemed convincing, even though it was wrong- same thing with calculus, I'm guessing.

Friendly reminder Wolfram Alpha exists if someone is having trouble with calculus. It not only solves the problem, but it shows you how it solved it step-by-step so it's a good study tool too.

rabbit leaps at the assailant, decapitating them within seconds

As with a great many things in history, it took a colossal effort to convince people of what think now as an obvious truth: "Poopy water bad."