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

Problem 2.1103 · medium

1. \[ \frac{d}{d x} 2 x \left(3 - x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 2 x^{2} + 6 x\right) \]
   algebraExpand the expression.✓ Proved
3. \[ = \frac{d}{d x} 6 x - \frac{d}{d x} 2 x^{2} \]
   sumApply the difference rule.✓ Proved
4. \[ = 6 \frac{d}{d x} x - 2 \frac{d}{d x} x^{2} \]
   constantApply the constant multiple rule.✓ Proved
5. \[ = 6 - 2 \frac{d}{d x} x^{2} \]
   derivative algebraDifferentiate the first term. Simplify the first term.✓ Proved
6. \[ = 6 - 4 x \]
   power algebraApply the power rule to the second term. Multiply the constants.✓ Proved