Derivative of \( \displaystyle 6 x \left(3 x^{2} + 3 x + 1\right) \)

Problem 2.997 · hard

1. \[ \frac{d}{d x} 6 x \left(3 x^{2} + 3 x + 1\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(18 x^{3} + 18 x^{2} + 6 x\right) \]
   algebraDistribute 6*x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 6 x + \frac{d}{d x} 18 x^{2} + \frac{d}{d x} 18 x^{3} \]
   sumApply the sum rule for derivatives.✓ Proved
4. \[ = 6 \frac{d}{d x} x + 18 \frac{d}{d x} x^{2} + 18 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 54 x^{2} + 36 x + 6 \]
   power algebraApply the power rule to each term. Multiply the coefficients.✓ Proved