Derivative of \( \displaystyle 5 \operatorname{atan}{\left(x + 1 \right)} \)

Problem 2.572 · medium

1. \[ \frac{d}{d x} 5 \operatorname{atan}{\left(x + 1 \right)} \]
   Start with the derivative of the function.✓ Proved
2. \[ = 5 \frac{d}{d x} \operatorname{atan}{\left(x + 1 \right)} \]
   constantPull the constant out of the derivative.✓ Proved
3. \[ = \frac{5 \frac{d}{d x} \left(x + 1\right)}{\left(x + 1\right)^{2} + 1} \]
   inverse-trigApply the derivative rule for arctan.✓ Proved
4. \[ = \frac{5}{\left(x + 1\right)^{2} + 1} \]
   derivative simplifyDifferentiate the inner function x + 1. Simplify the expression.✓ Proved