Derivative of \( \displaystyle \left(3 x - 12\right) e^{x - 3} \)

Problem 2.674 · medium

1. \[ \frac{d}{d x} \left(3 x - 12\right) e^{x - 3} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \left(3 x - 12\right) \frac{d}{d x} e^{x - 3} + 3 e^{x - 3} \frac{d}{d x} \left(x - 4\right) \]
   productApply the product rule.✓ Proved
3. \[ = \left(3 x - 12\right) \frac{d}{d x} e^{x - 3} + 3 e^{x - 3} \]
   derivativeDifferentiate the first part of the product.✓ Proved
4. \[ = \left(3 x - 12\right) e^{x - 3} \frac{d}{d x} \left(x - 3\right) + 3 e^{x - 3} \]
   chainApply the chain rule to the exponential term.✓ Proved
5. \[ = \left(3 x - 12\right) e^{x - 3} + 3 e^{x - 3} \]
   derivative algebraDifferentiate the exponent. Simplify the expression.✓ Proved
6. \[ = 3 \left(x - 3\right) e^{x - 3} \]
   algebra simplifyFactor out the common term 3*exp(x - 3). Simplify the remaining term.✓ Proved