Derivative of \( \displaystyle x \left(- 25 x^{2} - 30 x - 12\right) \)

Problem 2.1165 · hard

1. \[ \frac{d}{d x} x \left(- 25 x^{2} - 30 x - 12\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = x \frac{d}{d x} \left(- 25 x^{2} - 30 x - 12\right) + \left(- 25 x^{2} - 30 x - 12\right) \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
3. \[ = - 25 x^{2} + x \frac{d}{d x} \left(- 25 x^{2} - 30 x - 12\right) - 30 x - 12 \]
   derivative constantDifferentiate the first part of the product. The derivative of x is 1.✓ Proved
4. \[ = - 25 x^{2} + x \left(- 50 x - 30\right) - 30 x - 12 \]
   derivativeDifferentiate the polynomial term by term.✓ Proved
5. \[ = - 75 x^{2} - 60 x - 12 \]
   algebra simplifyDistribute x into the parenthesis. Combine like terms.✓ Proved