Derivative of \( \displaystyle \left(2 x - 8\right) e^{x - 3} \)

Problem 2.131 · hard

1. \[ \frac{d}{d x} \left(2 x - 8\right) e^{x - 3} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 2 \frac{d}{d x} \left(x - 4\right) e^{x - 3} \]
   constant-multiplePull out the constant factor 2.✓ Proved
3. \[ = 2 \left(x - 4\right) \frac{d}{d x} e^{x - 3} + 2 e^{x - 3} \frac{d}{d x} \left(x - 4\right) \]
   productApply the product rule.✓ Proved
4. \[ = 2 \left(x - 4\right) \frac{d}{d x} e^{x - 3} + 2 e^{x - 3} \]
   derivativeDifferentiate the first part of the product.✓ Proved
5. \[ = 2 \left(x - 4\right) e^{x - 3} + 2 e^{x - 3} \]
   chainApply the chain rule to the exponential term.✓ Proved
6. \[ = 2 \left(x - 3\right) e^{x - 3} \]
   algebra simplifyFactor out the common term exp(x - 3). Simplify the expression inside the parentheses.✓ Proved