{"id":"study-calc-chain-rule-hint-questions","audience":"high-school","category":"studying","technique":"constraints","track":"study","title":"Get tutor-style hints on a chain rule mistake","free":false,"task":"You got a chain rule derivative wrong on your AP Calculus homework and want to find the mistake yourself. Get exactly 3 numbered hint questions, under 55 words total, plain text, with no correct derivative, no worked steps and no explanation. The first question should point you to the inside function, and all of them must be about this problem.","materialLabel":"The problem and your work (attached to your prompt automatically)","material":"AP CALC AB - HW 3.4 - Chain rule - #12\n\nFind the derivative: f(x) = (3x^2 + 5)^4\n\nMY WORK:\nf'(x) = 4(3x^2 + 5)^3\nThat's what I got. The answer key at the back says something longer, I covered it with a sticky note because I want to figure it out.\n\nMs. Okonkwo's chain rule notes:\n- \"Outside, then inside.\" Take the derivative of the outside function, keep the inside the same, THEN multiply by the derivative of the inside.\n- Ask yourself: what's the inside function here? What's its derivative?\n- Common mistake: forgetting to multiply by the inside's derivative.\n\nMy friend Raúl says \"just use the power rule, it's the same thing.\" I don't think that's totally right.\n\nQuiz on 3.4 Thursday. Test on Unit 3 next Friday.","rules":[{"type":"numberedItems","count":3},{"type":"maxWords","max":55},{"type":"plainText"}],"mistakes":[{"title":"Asking for help","why":"The AI's default is to work the whole derivative out for you.","fix":"Say: \"Don't solve it. Only ask me questions.\"","checks":["r0","r1"]},{"title":"Not saying how many questions","why":"The AI picks its own number, and it usually picks more questions than you need.","fix":"Be exact: \"Exactly 3 numbered questions.\"","checks":["numberedItems"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each one: \"each question under 15 words.\"","checks":["maxWords"]},{"title":"Not saying where to start","why":"The AI may open with a general calculus tip instead of the step you skipped.","fix":"Add: \"The first question should point me to the inside function.\"","checks":["r2"]},{"title":"Forgetting where it will be read","why":"AI formats for a screen, with bold and headings that show up as stray symbols in your notes.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Says how many questions","patterns":["\\b(3|three)\\b.{0,25}question"]},{"label":"Says not to give the answer","patterns":["(don't|do not|never|no).{0,25}(answer|solution|solve|tell me|give)","only (ask|question|hint)"]},{"label":"Points to the key step","patterns":["inside","inner"]},{"label":"Sets a length limit","patterns":["\\d+\\s*words","word (limit|count)","under \\d+"]},{"label":"Asks for plain text","patterns":["plain","no bold","no markdown","no formatting","no headings"]}],"hint":"A tutor asks, they don't tell. Say you want only questions, how many and how short, and which part of the problem the first one should make you look at.","rubricLabels":["Contains only questions: no statements, explanations, worked steps or encouragement before, between or after them","Never gives the correct derivative, the factor 6x, or a finished expression the student could copy","The first question points the student to the inside function (3x^2 + 5) or its derivative, and every question is about this problem"]}