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

Problem 2.676 · medium

1. \[ \frac{d}{d x} \left(2 - x\right) e^{2 x - 3} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \left(2 - x\right) \frac{d}{d x} e^{2 x - 3} + e^{2 x - 3} \frac{d}{d x} \left(2 - x\right) \]
   productApply the product rule.✓ Proved
3. \[ = \left(2 - x\right) \frac{d}{d x} e^{2 x - 3} - e^{2 x - 3} \]
   derivativeDifferentiate the first term.✓ Proved
4. \[ = \left(2 - x\right) e^{2 x - 3} \frac{d}{d x} \left(2 x - 3\right) - e^{2 x - 3} \]
   chainApply the chain rule to the exponential term.✓ Proved
5. \[ = 2 \left(2 - x\right) e^{2 x - 3} - e^{2 x - 3} \]
   derivativeDifferentiate the inner function 2*x - 3.✓ Proved
6. \[ = \left(4 - 2 x\right) e^{2 x - 3} - e^{2 x - 3} \]
   algebraDistribute the 2.✓ Proved
7. \[ = \left(3 - 2 x\right) e^{2 x - 3} \]
   algebra simplifyFactor out the exponential term. Combine like terms.✓ Proved