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Derivative rules from a table of values

Problem 2.1643 · easy

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

Constant multiples and sums differentiate term by term.
\[ \left(-4\right) 4 - 3 \cdot 3 = -25 \]
Read the values from the table and substitute.✓ Proved

Answer \( h'(1) = -25 \)

Lines: 1 proved, 1 not checked. 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.

The full receipt

Line	Status	Checked by	Detail
1	Not checked	—	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: fail (error) — The solution fails to explicitly state the differentiation rule h'(x) = -3f'(x) - 4g'(x) before substituting values, jumping directly to arithmetic. While the arithmetic is correct, the logical step of applying the linearity of the derivative to the specific function h(x) is missing from the text, making the derivation incomplete.

Every verdict on record (4)

qwen3.6:27b-mlx: fail (error) 2026-10-05 — The solution fails to explicitly state the differentiation rule h'(x) = -3f'(x) - 4g'(x) before substituting values, jumping directly to arithmetic. While the arithmetic is correct, the logical step of applying the linearity of the derivative to the specific function h(x) is missing from the text, making the derivation incomplete.
gpt-oss:20b: pass 2026-10-05
qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly applies the linearity of differentiation and substitutes the values from the table accurately.
gpt-oss:20b: pass 2026-10-05

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 2026-10-05 with SymPy 1.14.0.