Home›Calculus 1›Derivatives of exponential functions›Problem 2.1184

Derivative of \( \displaystyle \frac{5 e^{2 x - 3}}{2} \)

Problem 2.1184 · medium Video

Differentiate \( \displaystyle f(x) = \frac{5 e^{2 x - 3}}{2} \).

\[ \frac{d}{d x} \frac{5 e^{2 x - 3}}{2} \]
Start with the derivative of the function.✓ Proved
\[ = \frac{5 \frac{d}{d x} e^{2 x - 3}}{2} \]
constant-multiplePull out the constant factor.✓ Proved
\[ = \frac{5 e^{2 x - 3} \frac{d}{d x} \left(2 x - 3\right)}{2} \]
chainApply the chain rule.✓ Proved
\[ = 5 e^{2 x - 3} \]
derivative algebraDifferentiate the inner function. Simplify the expression by multiplying the constants.✓ Proved

Answer \( 5 e^{2 x - 3} \)

Top: the graph of f = 5e^(2x - 3)/2. A tangent line slides along it, and its slope is plotted below as it goes, tracing f' = 5e^(2x - 3).

✓ 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. How we verify

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
4	✓ Proved	sympy 1.14.0	simplify(a - b) reduced to 0
5	✓ 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
qwen3.6:27b-mlx: pass

Every verdict on record (6)

qwen3.6:27b-mlx: pass 2026-10-03
gpt-oss:20b: pass 2026-10-03
qwen3.6:27b-mlx: pass 2026-09-29 — The solution correctly applies the constant multiple rule, chain rule, and basic derivative rules in separate steps. The labels are accurate and the logic is sound.
gpt-oss:20b: fail (style) 2026-09-29 — Step 1 uses an unlabelled rule; it should be labeled "derivative" to match the vocabulary and maintain the one‑rule‑per‑step rule.
qwen3.6:27b-mlx: pass 2026-09-29
gpt-oss:20b: pass 2026-09-29

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 2026-10-03 with SymPy 1.14.0.