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

Problem 2.68 · easy

1. \[ \frac{d}{d x} x \left(3 x + 2\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(3 x^{2} + 2 x\right) \]
   algebra algebraDistribute x into the parentheses. Simplify the terms.✓ Proved
3. \[ = \frac{d}{d x} 2 x + \frac{d}{d x} 3 x^{2} \]
   sumApply the sum rule.✓ Proved
4. \[ = 2 \frac{d}{d x} x + 3 \frac{d}{d x} x^{2} \]
   constant-multiplePull out the constants.✓ Proved
5. \[ = 6 x + 2 \]
   power algebraApply the power rule to each term. Multiply the terms.✓ Proved