Home›Calculus 1›Derivatives of exponential functions›Problem 2.274

Derivative of \( \displaystyle - e^{x} \)

Problem 2.274 · easy Mental math

Differentiate \( \displaystyle f(x) = - e^{x} \).

\[ \frac{d}{d x} \left(- e^{x}\right) \]
derivativeStart with the derivative of the function.✓ Proved
\[ = - \frac{d}{d x} e^{x} \]
constantMove the constant factor out of the derivative.✓ Proved
\[ = - e^{x} \]
exponentialThe derivative of exp(x) is exp(x).✓ Proved

Answer \( - e^{x} \)

✓ 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: pass
deepseek-r1:70b: pass
qwen3.6:27b-mlx: fail (style) — Step 2 applies the constant multiple rule, but is labeled 'constant'. The label 'constant' typically refers to the derivative of a constant being zero, whereas 'constant-multiple' is the correct label for factoring out a constant coefficient.

Every verdict on record (12)

qwen3.6:27b-mlx: fail (style) 2026-09-20 — Step 2 applies the constant multiple rule, but is labeled 'constant'. The label 'constant' typically refers to the derivative of a constant being zero, whereas 'constant-multiple' is the correct label for factoring out a constant coefficient.
gpt-oss:20b: pass 2026-09-20
qwen3.6:27b-mlx: pass 2026-09-20
gpt-oss:20b: pass 2026-09-20
qwen3.6:27b-mlx: pass 2026-09-19
deepseek-r1:70b: pass 2026-09-19
gpt-oss:20b: pass 2026-09-19
qwen3.6:27b-mlx: fail (style) 2026-09-19 — Step 2 applies the constant-multiple rule, but the label 'constant' is incorrect; 'constant' typically refers to the derivative of a constant being zero, whereas 'constant-multiple' is the correct label for factoring out a scalar.
deepseek-r1:70b: pass 2026-09-19
gpt-oss:20b: pass 2026-09-19
gpt-oss:20b: pass 2026-09-17
deepseek-r1:70b: pass 2026-09-17

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.