Derivative of \( \displaystyle - 9 x^{3} - 9 x^{2} - 3 x \)

Problem 2.1842 · medium

1. \[ \frac{d}{d x} \left(- 9 x^{3} - 9 x^{2} - 3 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 3 x\right) + \frac{d}{d x} \left(- 9 x^{2}\right) + \frac{d}{d x} \left(- 9 x^{3}\right) \]
   sumApply the sum rule to differentiate each term separately.✓ Proved
3. \[ = \frac{d}{d x} \left(- 3 x\right) + \frac{d}{d x} \left(- 9 x^{2}\right) - 9 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constant -9 from the first term.✓ Proved
4. \[ = \frac{d}{d x} \left(- 3 x\right) - 9 \frac{d}{d x} x^{2} - 9 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constant -9 from the second term.✓ Proved
5. \[ = - 3 \frac{d}{d x} x - 9 \frac{d}{d x} x^{2} - 9 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constant -3 from the third term.✓ Proved
6. \[ = - 27 x^{2} - 18 x - 3 \]
   power algebraApply the power rule to each term. Multiply the constants through the parentheses.✓ Proved