Derivative of \( \displaystyle 2 x \left(3 x + 2\right) \)

Problem 2.123 · easy

1. \[ \frac{d}{d x} 2 x \left(3 x + 2\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 2 x \frac{d}{d x} \left(3 x + 2\right) + \left(3 x + 2\right) \frac{d}{d x} 2 x \]
   productApply the product rule.✓ Proved
3. \[ = 2 x \frac{d}{d x} \left(3 x + 2\right) + 6 x + 4 \]
   constant-multipleFactor out the constant 2 from the first term.✓ Proved
4. \[ = 2 x \left(\frac{d}{d x} 2 + \frac{d}{d x} 3 x\right) + 6 x + 4 \]
   sumApply the sum rule to the second term.✓ Proved
5. \[ = 2 x \left(\frac{d}{d x} 2 + 3\right) + 6 x + 4 \]
   derivativeDifferentiate 3*x.✓ Proved
6. \[ = 12 x + 4 \]
   derivative algebra algebra algebraDifferentiate the constant 2. Simplify the expression. Distribute the 2. Combine like terms.✓ Proved