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

Problem 2.1597 · medium

1. \[ \frac{d}{d x} \left(4 x^{3} - 6 x^{2} + 3 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 3 x - \frac{d}{d x} 6 x^{2} + \frac{d}{d x} 4 x^{3} \]
   sumApply the sum rule to differentiate term by term.✓ Proved
3. \[ = 3 \frac{d}{d x} x - 6 \frac{d}{d x} x^{2} + 4 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants from each derivative.✓ Proved
4. \[ = 12 x^{2} - 12 x + 3 \]
   power algebraApply the power rule to each term. Multiply the constants and simplify the expression.✓ Proved