Derivative of \( \displaystyle 5 x e^{x + 1} \)

Problem 2.231 · hard

1. \[ \frac{d}{d x} 5 x e^{x + 1} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 5 \frac{d}{d x} x e^{x + 1} \]
   constant-multiplePull out the constant factor 5.✓ Proved
3. \[ = 5 x \frac{d}{d x} e^{x + 1} + 5 e^{x + 1} \frac{d}{d x} x \]
   productApply the product rule to x * exp(x + 1).✓ Proved
4. \[ = 5 x \frac{d}{d x} e^{x + 1} + 5 e^{x + 1} \]
   derivativeDifferentiate x with respect to x.✓ Proved
5. \[ = 5 x e^{x + 1} \frac{d}{d x} \left(x + 1\right) + 5 e^{x + 1} \]
   chainApply the chain rule to exp(x + 1).✓ Proved
6. \[ = 5 x e^{x + 1} + 5 e^{x + 1} \]
   derivative algebraDifferentiate x + 1 with respect to x. Simplify the expression inside the parentheses.✓ Proved
7. \[ = 5 \left(x + 1\right) e^{x + 1} \]
   simplifyFactor out the common term exp(x + 1).✓ Proved