Derivative of \( \displaystyle 15 x \left(3 x^{2} + 3 x + 1\right) \)

Problem 2.984 · hard

1. \[ \frac{d}{d x} 15 x \left(3 x^{2} + 3 x + 1\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(45 x^{3} + 45 x^{2} + 15 x\right) \]
   algebraDistribute 15*x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 15 x + \frac{d}{d x} 45 x^{2} + \frac{d}{d x} 45 x^{3} \]
   sumApply the sum rule for derivatives.✓ Proved
4. \[ = 15 \frac{d}{d x} x + 45 \frac{d}{d x} x^{2} + 45 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 135 x^{2} + 90 x + 15 \]
   power algebraApply the power rule to each term. Multiply the coefficients.✓ Proved