Derivative of \( \displaystyle \cos^{3}{\left(2 x \right)} \)

Problem 2.373 · medium

1. \[ \frac{d}{d x} \cos^{3}{\left(2 x \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 3 \cos^{2}{\left(2 x \right)} \frac{d}{d x} \cos{\left(2 x \right)} \]
   powerApply the power rule.✓ Proved
3. \[ = - 3 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \frac{d}{d x} 2 x \]
   chainApply the chain rule to the inner function.✓ Proved
4. \[ = - 6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \]
   derivative algebraDifferentiate the innermost function. Multiply the constants together.✓ Proved