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

Problem 2.646 · hard

1. \[ \frac{d}{d x} 2 x \left(25 x^{2} + 30 x + 12\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(50 x^{3} + 60 x^{2} + 24 x\right) \]
   algebraDistribute the 2*x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 24 x + \frac{d}{d x} 60 x^{2} + \frac{d}{d x} 50 x^{3} \]
   sumApply the sum rule for derivatives.✓ Proved
4. \[ = 24 \frac{d}{d x} x + 60 \frac{d}{d x} x^{2} + 50 \frac{d}{d x} x^{3} \]
   constant-multiplePull out the constant coefficients.✓ Proved
5. \[ = 150 x^{2} + 120 x + 24 \]
   power simplifyApply the power rule to each term. Multiply the constants to get the final result.✓ Proved