log(cos(x))
d --(log(cos(x))) dx
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
Now simplify:
The answer is:
-sin(x) -------- cos(x)
/ 2 \ | sin (x)| -|1 + -------| | 2 | \ cos (x)/
/ 2 \ | sin (x)| -2*|1 + -------|*sin(x) | 2 | \ cos (x)/ ----------------------- cos(x)