Derivative of \( \displaystyle e^{3 x + 5} \)

Problem 2.364 · easy

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