Chat GPT 4 and calculus: Experiences?

So if I am not mistaken, OpenAI has taken down the plugins and therefore the plugin of Wolfram Alpha is not present. However, I gave ChatGPT some basic calculus steps, where I wrongly thought that 2- (2/t) leads to (t+1)/t. There was an obvious mistake and I could not see it. I had mistaken a multipication sign for a minus sign.
However, ChatGPT could not tell. When asked separately if the first terms leads to the second one, he could tell no but in my calcualtion he could not find the mistake, eventhough it was basic calculus. Shouldn’t AI be quite good in basic caluculus as there is kind of like always the same pattern to follow?

Or is it just that bad after the new update?

Don’t be so fast to shoot ChatGPT down or LLMs for that matter.


Prompt

Create the rules of calculus derivatives for Prolog then show step by step how to calculate the derivative of 2-(2/t)

Completion

Creating a Prolog program to handle calculus derivatives involves defining rules that capture the basic principles of differentiation. In Prolog, we can define rules for the derivative of constants, power functions, addition, subtraction, multiplication, division, and more complex functions as needed.

For the task at hand, let’s focus on the necessary rules to differentiate the function 2 - (2/t). We need rules for constants, subtraction, and division. Here’s a simplified version:

  1. Derivative of a Constant: The derivative of a constant is zero.
  2. Derivative of a Variable (like t): The derivative of t with respect to t is 1.
  3. Derivative of Subtraction: The derivative of f - g is the derivative of f minus the derivative of g.
  4. Derivative of Division: The derivative of u/v is (v * du/dt - u * dv/dt) / v^2, where du/dt is the derivative of u with respect to t, and dv/dt is the derivative of v with respect to t.

Let’s define these rules in Prolog:

% Derivative of a constant is 0
derivative(C, t, 0) :- number(C).

% Derivative of t with respect to t is 1
derivative(t, t, 1).

% Derivative of subtraction
derivative(U - V, t, DU - DV) :-
    derivative(U, t, DU),
    derivative(V, t, DV).

% Derivative of division
derivative(U / V, t, (V * DU - U * DV) / (V * V)) :-
    derivative(U, t, DU),
    derivative(V, t, DV).

Now, let’s calculate the derivative of 2 - (2/t) step by step:

  1. Apply the Subtraction Rule:

    • f = 2 and g = 2/t
    • df/dt = derivative of 2 and dg/dt = derivative of 2/t
  2. Calculate df/dt:

    • 2 is a constant, so its derivative is 0.
  3. Calculate dg/dt:

    • Apply the Division Rule to 2/t:
      • u = 2 (constant) and v = t
      • du/dt = derivative of 2 (which is 0)
      • dv/dt = derivative of t (which is 1)
    • So, dg/dt = (t * 0 - 2 * 1) / t^2 = -2 / t^2.
  4. Combine the Results:

    • The derivative of 2 - (2/t) is 0 - (-2 / t^2), which simplifies to 2 / t^2.

In Prolog, you would query this as:

?- derivative(2 - (2 / t), t, Result).

And the expected output should be:

Result = 2 / t^2.

This Prolog program is a basic implementation and works for the given function. For more complex functions, additional rules (like for exponentiation, trigonometric functions, etc.) would need to be added.


To cross check using Wolfram

image


Related post

Define a Prolog predicate that calculates the derivative of a mathematical expression

Yeah, its good at computing maybe the derivative but it hardly can tell the mistake in my calculations. And as I said, even if the mistake is quite obvious.

In all honesty, your inquiry lacks some necessary details for a comprehensive assessment. It’s essential to consider whether the issue lies with ChatGPT or if it might be related to the way you formulated your question.

As a moderator, I frequently encounter similar concerns from users. It’s important to ensure fairness in these situations. :slightly_smiling_face:

Yeah, but I was not seeking for a solution for my specific problem because I did not want to write my own caluclus computation here and and then find a solution about it or any similar stuff. I just wanted to see if anyone has noticed anything similar with weaknesses of ChatGPT when it comes to corrections or dealing with calculus. Cause if it is not the case, then it may be of course possible that my prompts are just not good but I really doubt that cause I use it quite frequently and know the one or other trick. But yeah, it could be a mistake in my prompts as well. I am not ruling that out.

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Thank you for bringing up your observations about ChatGPT’s performance in corrections and calculus-related queries.

I’ve taken note of your feedback. Regarding the title, I appreciate your input. Could you please use a title that you think would better reflect the essence you’re aiming for? I’m here to ensure your experience is as positive as possible! :blush:

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Changed the title. Seems more appropriate now? :slight_smile:

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I’m using ChatGPT4 as a study aid with an undergraduate maths course, including calculus. When I started last year it was really helpful in providing clear explanations of points I was finding difficult. As an autistic person I found the patience and the ability to ask for clarification really helpful and was recommending it to others. More recently, however, ChatGPT4 has tended to go off into long rambling explanations which don’t seem to come to any conclusion. Something has cahnged, and it is not for the better.

derivative I just wanted to see if anyone has noticed anything similar with weaknesses of ChatGPT when it comes to corrections or dealing with calculus.