Derivative of \( \displaystyle - 3 \ln{\left(\cos{\left(x \right)} \right)} \)

Problem 2.197 · hard

1. \[ \frac{d}{d x} \left(- 3 \ln{\left(\cos{\left(x \right)} \right)}\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = - 3 \frac{d}{d x} \ln{\left(\cos{\left(x \right)} \right)} \]
   constant-multiplePull the constant out of the derivative.✓ Proved
3. \[ = - \frac{3 \frac{d}{d x} \cos{\left(x \right)}}{\cos{\left(x \right)}} \]
   chainApply the chain rule for the logarithm.✓ Proved
4. \[ = \frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} \]
   derivative algebraDifferentiate the inner function cos(x). Simplify the signs and the fraction.✓ Proved
5. \[ = 3 \tan{\left(x \right)} \]
   simplifyUse the identity sin(x)/cos(x) = tan(x).✓ Proved