On all R, F has ascending rational coefficients [3/1, 8/1, -14/3, 17/4, -3/1]. Give its complete normalized ascending derivative coefficients as reduced fractions.
G001 — On all R, F has ascending rational coefficients [3/1, 8/1, -14/3, 17/4, -3/1]. Give its complete normalized ascending derivative coefficients as reduced fractions.
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention.
Raw integer f has length1..4 and rational candidate F length1..5.Every raw number is SAFE;rational denominators are STRICTLY positive,not repaired from negatives.Trim only trailing zeros,keeping a singleton zero polynomial.Derived algebra has no1e6 or raw-degree cap.
Primitive candidate ORIGINAL derivative degree0 := mul(1, 8)
After
Primitive candidate ORIGINAL derivative degree0 = 8
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Primitive candidate ORIGINAL derivative degree1 := mul(2, -14/3)
After
Primitive candidate ORIGINAL derivative degree1 = -28/3
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Primitive candidate ORIGINAL derivative degree2 := mul(3, 17/4)
After
Primitive candidate ORIGINAL derivative degree2 = 51/4
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Primitive candidate ORIGINAL derivative degree3 := mul(4, -3)
After
Primitive candidate ORIGINAL derivative degree3 = -12
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Differentiate EVERY nonconstant term into i*c_i*x^(i-1),list the COMPLETE ascending coefficients,and trim trailing zeros.Constants differentiate to0,so a constant candidate returns[0/1],not[].No input f was provided;do not invent a Yes/No eligibility test F_prime=f.
S007 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.
S006 · premise_and_result_audit — Recompute Primitive candidate ORIGINAL derivative degree3 with exact rational arithmetic, not rounded decimals.
S005 · premise_and_result_audit — Recompute Primitive candidate ORIGINAL derivative degree2 with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute Primitive candidate ORIGINAL derivative degree1 with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Primitive candidate ORIGINAL derivative degree0 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.
S001 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.
Result
[8/1, -28/3, 51/4, -12/1]
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.