Derivative of \( \displaystyle \left(5 x - 5\right) e^{x} \)

Problem 2.307 · medium

1. \[ \frac{d}{d x} \left(5 x - 5\right) e^{x} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 5 \frac{d}{d x} \left(x - 1\right) e^{x} \]
   constant-multiplePull out the constant factor 5.✓ Proved
3. \[ = 5 \left(x - 1\right) \frac{d}{d x} e^{x} + 5 e^{x} \frac{d}{d x} \left(x - 1\right) \]
   productApply the product rule to the remaining terms.✓ Proved
4. \[ = 5 \left(x - 1\right) \frac{d}{d x} e^{x} + 5 e^{x} \]
   derivative simplifyDifferentiate the first part of the product (x - 1). Simplify the derivative of (x - 1).✓ Proved
5. \[ = 5 \left(x - 1\right) e^{x} + 5 e^{x} \]
   exponentialDifferentiate the exponential term.✓ Proved
6. \[ = 5 x e^{x} \]
   algebra simplify simplifyDistribute the exponential term. Combine like terms. Final simplified form.✓ Proved