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

Problem 2.661 · medium

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