Derivative of \( \displaystyle - 4 x^{3} + 6 x^{2} - 3 x \)

Problem 2.1585 · medium

1. \[ \frac{d}{d x} \left(- 4 x^{3} + 6 x^{2} - 3 x\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = - \frac{d}{d x} 3 x + \frac{d}{d x} 6 x^{2} + \frac{d}{d x} \left(- 4 x^{3}\right) \]
   sumApply the sum rule to differentiate each term separately.✓ Proved
3. \[ = - 3 \frac{d}{d x} x + 6 \frac{d}{d x} x^{2} - 4 \frac{d}{d x} x^{3} \]
   constant-multiplePull out the constant coefficients.✓ Proved
4. \[ = - 12 x^{2} + 12 x - 3 \]
   power simplifyApply the power rule to each term. Simplify the resulting expression.✓ Proved