Derivative of \( \displaystyle 2 e^{x} \)
Problem 2.389 · easy Mental math
Differentiate \( \displaystyle f(x) = 2 e^{x} \).
- \[ \frac{d}{d x} 2 e^{x} \]Start with the derivative of the function.✓ Proved
- \[ = 2 \frac{d}{d x} e^{x} \]constant-multiplePull the constant out of the derivative.✓ Proved
- \[ = 2 e^{x} \]exponentialThe derivative of exp(x) is exp(x).✓ Proved
Answer \( 2 e^{x} \)
✓ Nihil obstat Every line of this solution was proved by the computer algebra system SymPy. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | ✓ Proved | sympy 1.14.0 | line 1 is the problem as stated |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| 3 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| answer | ✓ Proved | sympy 1.14.0 | final line against the stated answer: simplify(a - b) reduced to 0 |
| answer, a second way | ✓ Proved | sympy 1.14.0 | SymPy differentiated f directly and got the stated answer |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: pass
Every verdict on record (6)
qwen3.6:27b-mlx: pass 2026-09-21gpt-oss:20b: pass 2026-09-21qwen3.6:27b-mlx: pass 2026-09-20gpt-oss:20b: fail (style) 2026-09-20 — Step 1 is labeled "unlabelled" but it applies the constant‑multiple rule (pulling the constant 2 out of the derivative). The correct label should be "constant‑multiple". The subsequent step then correctly applies the "exponential" rule.qwen3.6:27b-mlx: pass 2026-09-20gpt-oss:20b: pass 2026-09-20
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
gemma4:26b, checked 2026-09-26 with SymPy 1.14.0.