Derivative of \( \displaystyle \frac{\operatorname{atan}{\left(3 x - 1 \right)}}{3} \)

Problem 2.644 · medium

1. \[ \frac{d}{d x} \frac{\operatorname{atan}{\left(3 x - 1 \right)}}{3} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \operatorname{atan}{\left(3 x - 1 \right)}}{3} \]
   constant-multiplePull out the constant factor 1/3.✓ Proved
3. \[ = \frac{\frac{d}{d x} \left(3 x - 1\right)}{3 \left(\left(3 x - 1\right)^{2} + 1\right)} \]
   chainApply the chain rule to the arctangent function.✓ Proved
4. \[ = \frac{1}{\left(3 x - 1\right)^{2} + 1} \]
   derivative simplifyDifferentiate the inner linear function. Simplify the expression by canceling the 3.✓ Proved