Derivative of \( \displaystyle - 16 x^{3} - 24 x^{2} - 12 x \)

Problem 2.1507 · medium

1. \[ \frac{d}{d x} \left(- 16 x^{3} - 24 x^{2} - 12 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 12 x\right) + \frac{d}{d x} \left(- 24 x^{2}\right) + \frac{d}{d x} \left(- 16 x^{3}\right) \]
   sumApply the sum rule.✓ Proved
3. \[ = - 12 \frac{d}{d x} x - 24 \frac{d}{d x} x^{2} - 16 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants.✓ Proved
4. \[ = - 48 x^{2} - 48 x - 12 \]
   power algebra simplifyApply the power rule to each term. Multiply the constants. Factor out the greatest common divisor.✓ Proved