Derivative of \( \displaystyle 3 x \left(3 x^{2} - 3 x + 1\right) \)

Problem 2.98 · hard

1. \[ \frac{d}{d x} 3 x \left(3 x^{2} - 3 x + 1\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = 3 x \frac{d}{d x} \left(3 x^{2} - 3 x + 1\right) + \left(3 x^{2} - 3 x + 1\right) \frac{d}{d x} 3 x \]
   productApply the product rule.✓ Proved
3. \[ = 9 x^{2} + 3 x \frac{d}{d x} \left(3 x^{2} - 3 x + 1\right) - 9 x + 3 \]
   constant-multipleDifferentiate the first part of the product.✓ Proved
4. \[ = 9 x^{2} + x \left(18 x - 9\right) - 9 x + 3 \]
   derivative algebraDifferentiate the second part of the product. Distribute the 3 in the first term.✓ Proved
5. \[ = 27 x^{2} - 18 x + 3 \]
   algebra simplifyDistribute the 3*x in the second term. Combine like terms.✓ Proved