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

Problem 2.1416 · medium

1. \[ \frac{d}{d x} x \left(2 - 3 x\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 3 x^{2} + 2 x\right) \]
   algebraDistribute x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 2 x - \frac{d}{d x} 3 x^{2} \]
   sumApply the difference rule.✓ Proved
4. \[ = 2 \frac{d}{d x} x - 3 \frac{d}{d x} x^{2} \]
   constantPull out the constant coefficient.✓ Proved
5. \[ = 2 - 3 \frac{d}{d x} x^{2} \]
   derivativeDifferentiate the first term.✓ Proved
6. \[ = 2 - 6 x \]
   power algebraApply the power rule to x**2. Multiply the constants.✓ Proved