Derivative of \( \displaystyle 18 x^{3} - 18 x^{2} + 6 x \)

Problem 2.1500 · medium

1. \[ \frac{d}{d x} \left(18 x^{3} - 18 x^{2} + 6 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 6 x - \frac{d}{d x} 18 x^{2} + \frac{d}{d x} 18 x^{3} \]
   sumApply the sum rule.✓ Proved
3. \[ = 6 \frac{d}{d x} x - 18 \frac{d}{d x} x^{2} + 18 \frac{d}{d x} x^{3} \]
   constant-multipleApply the constant multiple rule to each term.✓ Proved
4. \[ = 54 x^{2} - 36 x + 6 \]
   power algebraApply the power rule to each term. Multiply the constants.✓ Proved