On all R, f has ascending coefficients [1, 1], starting with its constant term. Find the derivative of (0)f at x=-2. Input degrees are at most three; retain all higher terms produced by the operation.
G001 — On all R, f has ascending coefficients [1, 1], starting with its constant term. Find the derivative of (0)f at x=-2. Input degrees are at most three; retain all higher terms produced by the operation.
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.
Check THIS source interface:distance uses ONLY its complete coordinate frame;other families use a domain.Discrete operations use local hyphens,legacy banks underscores.Retain family-specific ordered output types and original bilingual data/status.
Check RAW ascending coefficient arity1..4 and EVERY SAFE integer BEFORE trimming trailing zeros,retaining[0].The GIVEN whole polynomial law holds on R;sample values alone do not establish differentiability.
source roles = [f derivative at ORIGINAL x, [1], -2]
After
derived = [1]
Conditions: none
Evaluate ascending coefficients by Horner from the highest power,multiplying the DECLARED argument then adding the ORIGINAL coefficient at every step,including zeros.Do not replace an inner value with original x.
S009 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
S008 · premise_and_result_audit — Recompute Derivative scalar ORIGINAL c times fprime with exact rational arithmetic, not rounded decimals.
S007 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
S006 · premise_and_result_audit — Recompute f derivative at ORIGINAL x Horner power0 plus coefficient with exact rational arithmetic, not rounded decimals.
S005 · premise_and_result_audit — Recompute f derivative at ORIGINAL x Horner power0 times argument with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
S003 · premise_and_result_audit — Recompute f derivative coefficient power1 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
S001 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
Result
0
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.