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

Problem 2.989 · hard

1. \[ \frac{d}{d x} 15 x \left(3 x^{2} - 3 x + 1\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(45 x^{3} - 45 x^{2} + 15 x\right) \]
   algebraDistribute the 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 differentiation.✓ 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 from each term.✓ Proved
5. \[ = 135 x^{2} - 90 x + 15 \]
   power simplifyApply the power rule to each term. Multiply the coefficients to get the final result.✓ Proved