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

Problem 2.1130 · hard

1. \[ \frac{d}{d x} x \left(- 4 x^{2} - 6 x - 3\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = x \frac{d}{d x} \left(- 4 x^{2} - 6 x - 3\right) + \left(- 4 x^{2} - 6 x - 3\right) \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
3. \[ = - 4 x^{2} + x \frac{d}{d x} \left(- 4 x^{2} - 6 x - 3\right) - 6 x - 3 \]
   derivative constant-multipleDifferentiate the first part of the product. Simplify the first term.✓ Proved
4. \[ = - 4 x^{2} + x \left(- 8 x - 6\right) - 6 x - 3 \]
   derivativeDifferentiate the second part of the product.✓ Proved
5. \[ = - 12 x^{2} - 12 x - 3 \]
   algebra simplifyDistribute x into the parentheses. Combine like terms.✓ Proved