Derivative of \( \displaystyle e^{6 x + 8} \)

Problem 2.582 · easy

1. \[ \frac{d}{d x} e^{6 x + 8} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{6 x + 8} \frac{d}{d x} \left(6 x + 8\right) \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(\frac{d}{d x} 8 + \frac{d}{d x} 6 x\right) e^{6 x + 8} \]
   sumDifferentiate the sum inside the parentheses.✓ Proved
4. \[ = \left(\frac{d}{d x} 8 + 6\right) e^{6 x + 8} \]
   derivativeDifferentiate the linear term.✓ Proved
5. \[ = 6 e^{6 x + 8} \]
   constant simplifyThe derivative of a constant is zero. Simplify the final expression.✓ Proved