Derivative of \( \displaystyle 3 x e^{x} - 3 e^{x} \)

Problem 2.1599 · hard Beautiful

1. \[ \frac{d}{d x} \left(3 x e^{x} - 3 e^{x}\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 3 x e^{x} - \frac{d}{d x} 3 e^{x} \]
   sumApply the sum rule.✓ Proved
3. \[ = 3 \frac{d}{d x} x e^{x} - 3 \frac{d}{d x} e^{x} \]
   constant-multiple algebraFactor out the constant 3. Factor out the constant 3 from the expression.✓ Proved
4. \[ = 3 x \frac{d}{d x} e^{x} + 3 e^{x} \frac{d}{d x} x - 3 \frac{d}{d x} e^{x} \]
   productApply the product rule to the first term.✓ Proved
5. \[ = 3 x e^{x} \]
   derivative algebra simplify simplifyDifferentiate the individual components. Distribute the derivative results. Simplify the expression by canceling terms. Final simplified result.✓ Proved