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

Problem 2.524 · hard

1. \[ \frac{d}{d x} e^{\cos{\left(2 x \right)}} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{\cos{\left(2 x \right)}} \frac{d}{d x} \cos{\left(2 x \right)} \]
   chainApply the chain rule to the exponential function.✓ Proved
3. \[ = - e^{\cos{\left(2 x \right)}} \sin{\left(2 x \right)} \frac{d}{d x} 2 x \]
   trigDifferentiate the cosine function.✓ Proved
4. \[ = - 2 e^{\cos{\left(2 x \right)}} \sin{\left(2 x \right)} \]
   derivative simplifyDifferentiate the inner linear function. Simplify the final expression.✓ Proved