Derivative of \( \displaystyle \ln{\left(2 x - 3 \right)} \)

Problem 2.29 · medium

1. \[ \frac{d}{d x} \ln{\left(2 x - 3 \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \left(2 x - 3\right)}{2 x - 3} \]
   chainApply the chain rule for the logarithm.✓ Proved
3. \[ = \frac{- \frac{d}{d x} 3 + \frac{d}{d x} 2 x}{2 x - 3} \]
   sumDifferentiate the terms inside the parentheses separately.✓ Proved
4. \[ = \frac{2}{2 x - 3} \]
   constant algebra simplifyThe derivative of a constant is zero. Simplify the expression. Final simplified result.✓ Proved