Derivative of \( \displaystyle 6 x \left(2 x + 1\right) \)

Problem 2.1073 · medium

1. \[ \frac{d}{d x} 6 x \left(2 x + 1\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(12 x^{2} + 6 x\right) \]
   algebraExpand the expression first.✓ Proved
3. \[ = \frac{d}{d x} 6 x + \frac{d}{d x} 12 x^{2} \]
   sumApply the sum rule.✓ Proved
4. \[ = 6 \frac{d}{d x} x + 12 \frac{d}{d x} x^{2} \]
   constant-multiplePull out the constants.✓ Proved
5. \[ = 24 x + 6 \]
   power algebraDifferentiate the power terms. Simplify the final expression.✓ Proved