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

Problem 2.2076 · medium

1. \[ \frac{d}{d x} \left(- x^{3} - 3 x^{2} - 3 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 3 x\right) + \frac{d}{d x} \left(- 3 x^{2}\right) + \frac{d}{d x} \left(- x^{3}\right) \]
   sumApply the sum rule to differentiate each term separately.✓ Proved
3. \[ = - 3 \frac{d}{d x} x - 3 \frac{d}{d x} x^{2} - \frac{d}{d x} x^{3} \]
   constantFactor out the negative signs.✓ Proved
4. \[ = - 3 x^{2} - 6 x - 3 \]
   power algebraApply the power rule to each term. Simplify the coefficients.✓ Proved