Derivative of \( \displaystyle 2 x e^{4 x} \)

Problem 2.347 · medium

1. \[ \frac{d}{d x} 2 x e^{4 x} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 2 \frac{d}{d x} x e^{4 x} \]
   constant-multiplePull out the constant factor 2.✓ Proved
3. \[ = 2 x \frac{d}{d x} e^{4 x} + 2 e^{4 x} \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
4. \[ = 2 x \frac{d}{d x} e^{4 x} + 2 e^{4 x} \]
   derivative simplifyDifferentiate x. Simplify the expression.✓ Proved
5. \[ = 8 x e^{4 x} + 2 e^{4 x} \]
   chain algebraApply the chain rule to exp(4*x). Rearrange the terms.✓ Proved
6. \[ = 2 \left(4 x + 1\right) e^{4 x} \]
   simplifyFactor out the common term exp(4*x) and simplify.✓ Proved