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Derivative rules from a table of values

Problem 2.2505 · easy

Use the table to find \( \displaystyle h'(3) \) for \( \displaystyle h(x) = 2 f(x) + 4 g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 3 & -2 & -1 & 4 & 3\end{array} \]

Constant multiples and sums differentiate term by term.
Reviewed
\[ 2 \left(-1\right) + 4 \cdot 3 = 10 \]
Read the values from the table and substitute.✓ Proved

Answer \( h'(3) = 10 \)

Lines: 1 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. The reviewers disagree about how one step is explained; every verdict is in the receipt. How we verify

The full receipt

Line	Status	Checked by	Detail
1	Reviewed	reviewers: gpt-oss:20b, qwen3.6:27b-mlx	a sentence; read, not computed
2	✓ Proved	sympy 1.14.0	simplify(lhs - rhs) reduced to 0
answer, a second way	✓ Checked independently	sympy 1.14.0 + mpmath 1.3.0	differentiated concrete polynomials built to match the table

Reviewers

gpt-oss:20b: pass
qwen3.6:27b-mlx: pass — The solution correctly applies the linearity of differentiation and substitutes the values from the table accurately.

Every verdict on record (6)

qwen3.6:27b-mlx: pass 2026-10-26 — The solution correctly applies the linearity of differentiation and substitutes the values from the table accurately.
gpt-oss:20b: pass 2026-10-26
qwen3.6:27b-mlx: pass 2026-10-25 — The solution correctly applies the linearity of the derivative and substitutes the values from the table accurately.
gpt-oss:20b: pass 2026-10-25
qwen3.6:27b-mlx: fail (error) 2026-10-25 — The solution fails to explicitly state the differentiation rule (h'(x) = 2f'(x) + 4g'(x)) before substituting values. While the arithmetic is correct, the logical step connecting the problem statement to the numerical substitution is missing, making the derivation incomplete.
gpt-oss:20b: pass 2026-10-25

Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence, not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by generator:structured/derivative_from_table, checked 2026-10-26 with SymPy 1.14.0.