Derivative of \( \displaystyle \frac{2 e^{3 x - 1}}{3} \)

Problem 2.493 · medium

1. \[ \frac{d}{d x} \frac{2 e^{3 x - 1}}{3} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{2 \frac{d}{d x} e^{3 x - 1}}{3} \]
   constant-multiplePull out the constant factor.✓ Proved
3. \[ = \frac{2 e^{3 x - 1} \frac{d}{d x} \left(3 x - 1\right)}{3} \]
   chainApply the chain rule.✓ Proved
4. \[ = 2 e^{3 x - 1} \]
   derivative algebraDifferentiate the inner function 3*x - 1. Simplify the expression by multiplying the constants.✓ Proved