Derivative of \( \displaystyle 3 x \left(25 x^{2} + 30 x + 12\right) \)

Problem 2.831 · hard

1. \[ \frac{d}{d x} 3 x \left(25 x^{2} + 30 x + 12\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(75 x^{3} + 90 x^{2} + 36 x\right) \]
   algebraDistribute the 3*x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 36 x + \frac{d}{d x} 90 x^{2} + \frac{d}{d x} 75 x^{3} \]
   sumApply the sum rule for derivatives.✓ Proved
4. \[ = 36 \frac{d}{d x} x + 90 \frac{d}{d x} x^{2} + 75 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 225 x^{2} + 180 x + 36 \]
   power simplifyApply the power rule to each term. Multiply the constants to get the final result.✓ Proved