Derivative of \( \displaystyle 50 x^{3} - 30 x^{2} + 6 x \)
Problem 2.2421 · medium Video
Differentiate \( \displaystyle f(x) = 50 x^{3} - 30 x^{2} + 6 x \).
- \[ \frac{d}{d x} \left(50 x^{3} - 30 x^{2} + 6 x\right) \]derivativeStart with the derivative of the function.✓ Proved
- \[ = \frac{d}{d x} 6 x - \frac{d}{d x} 30 x^{2} + \frac{d}{d x} 50 x^{3} \]sumApply the sum rule to differentiate each term separately.✓ Proved
- \[ = 6 \frac{d}{d x} x - 30 \frac{d}{d x} x^{2} + 50 \frac{d}{d x} x^{3} \]constant-multiplePull out the constant coefficients.✓ Proved
- \[ = 150 x^{2} - 60 x + 6 \]power algebraApply the power rule to each term. Multiply the constants.✓ Proved
Answer \( 6 \left(5 x - 1\right)^{2} \)
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. 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 | ✓ 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: passqwen3.6:27b-mlx: pass
Every verdict on record (6)
qwen3.6:27b-mlx: pass 2026-10-19gpt-oss:20b: pass 2026-10-19qwen3.6:27b-mlx: pass 2026-10-16gpt-oss:20b: pass 2026-10-16qwen3.6:27b-mlx: pass 2026-10-16gpt-oss:20b: fail (error) 2026-10-16 — The stated answer 6*(5*x - 1)**2 does not equal the correct derivative 150*x**2 - 60*x + 6, so the solution contains a wrong final answer.
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 2026-10-19 with SymPy 1.14.0.