Derivative of \( \displaystyle 3 x \left(- 3 x^{2} - 6 x - 4\right) \)

Problem 2.1407 · hard

1. \[ \frac{d}{d x} 3 x \left(- 3 x^{2} - 6 x - 4\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = 3 x \frac{d}{d x} \left(- 3 x^{2} - 6 x - 4\right) + \left(- 3 x^{2} - 6 x - 4\right) \frac{d}{d x} 3 x \]
   productApply the product rule.✓ Proved
3. \[ = - 9 x^{2} + 3 x \frac{d}{d x} \left(- 3 x^{2} - 6 x - 4\right) - 18 x - 12 \]
   derivativeDifferentiate the first part of the product.✓ Proved
4. \[ = - 9 x^{2} - 3 x \frac{d}{d x} 4 - 3 x \frac{d}{d x} 6 x + 3 x \frac{d}{d x} \left(- 3 x^{2}\right) - 18 x - 12 \]
   sumDistribute the derivative over the sum.✓ Proved
5. \[ = - 27 x^{2} - 36 x - 12 \]
   derivative algebra constant-multiple simplifyDifferentiate each term in the sum. Simplify the terms. Distribute the 3. Combine like terms.✓ Proved