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

Problem 2.685 · easy

1. \[ \frac{d}{d x} \frac{e^{5 x + 1}}{5} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} e^{5 x + 1}}{5} \]
   constantPull out the constant factor 1/5.✓ Proved
3. \[ = \frac{e^{5 x + 1} \frac{d}{d x} \left(5 x + 1\right)}{5} \]
   chainApply the chain rule to the exponential function.✓ Proved
4. \[ = \frac{\left(\frac{d}{d x} 1 + \frac{d}{d x} 5 x\right) e^{5 x + 1}}{5} \]
   sumDifferentiate the sum inside the parentheses.✓ Proved
5. \[ = e^{5 x + 1} \]
   derivative algebra simplifyDifferentiate the terms inside the parentheses. Simplify the expression. Cancel the 5 in the numerator and denominator.✓ Proved