Derivative of \( \displaystyle \sin{\left(2 x + 1 \right)} \)

Problem 2.172 · medium

1. \[ \frac{d}{d x} \sin{\left(2 x + 1 \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \cos{\left(2 x + 1 \right)} \frac{d}{d x} \left(2 x + 1\right) \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(\frac{d}{d x} 1 + \frac{d}{d x} 2 x\right) \cos{\left(2 x + 1 \right)} \]
   sumDifferentiate the sum inside the parentheses.✓ Proved
4. \[ = \left(\frac{d}{d x} 1 + 2\right) \cos{\left(2 x + 1 \right)} \]
   derivativeDifferentiate 2*x.✓ Proved
5. \[ = 2 \cos{\left(2 x + 1 \right)} \]
   derivative algebraDifferentiate the constant 1. Simplify the expression.✓ Proved