Derivative of \( \displaystyle \ln{\left(\frac{\pi e^{- 3 x}}{4} \right)} \)

Problem 2.1145 · hard Beautiful

1. \[ \frac{d}{d x} \ln{\left(\frac{\pi e^{- 3 x}}{4} \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 3 x + \ln{\left(\frac{\pi}{4} \right)}\right) \]
   algebra algebraUse the logarithm product and quotient rules to split the terms. Simplify the logarithm of the exponential term.✓ Proved
3. \[ = - \frac{d}{d x} 3 x + \frac{d}{d x} \ln{\left(\frac{\pi}{4} \right)} \]
   sumSplit the derivative into two parts.✓ Proved
4. \[ = - \frac{d}{d x} 3 x \]
   constantThe derivative of a constant is zero.✓ Proved
5. \[ = -3 \]
   derivativeThe derivative of 3*x is 3.✓ Proved