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

Problem 2.40 · medium

1. \[ \frac{d}{d x} \left(2 x - 2\right) e^{x} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \left(2 x - 2\right) \frac{d}{d x} e^{x} + 2 e^{x} \frac{d}{d x} \left(x - 1\right) \]
   productApply the product rule to the terms.✓ Proved
3. \[ = \left(2 x - 2\right) e^{x} + 2 e^{x} \]
   derivative simplify algebraDifferentiate the individual parts. Simplify the first term. Distribute the 2 in the second term.✓ Proved
4. \[ = 2 x e^{x} \]
   algebra simplifyDistribute the exp(x) in the second term. Combine like terms.✓ Proved